Pherdnut

Man, hadn't played this one for years. It's pretty sweet. I haven't read through the whole thread but a few tips on the game I don't typically hear from years of excessive play.

I actually like turn based and never play real time, so keep this in mind when looking at my evaluation of things.

Yes, raid the cultists. In medium difficulty, I hit every building at least three times a week. If you don't need the money right away, sit on the psiclone for a while and then just dump it all at the end of the week. Wait until it goes back up in price or you won't get nearly as much for it. This is a good approach for all highly valuable items, especially alien artifacts.

Starting Base

I like to set up my first base with two additional physics labs and one additional bio. Finish the first availabe bio transport research ASAP. The physics labs won't really be that useful until the following week unless you're playing on superhuman and they start showing up with the larger UFOs sooner. With two bio labs, You'll have everythign you need for Toxigun Bs before you've even started researching bio warfare in the advanced lab which you should research at the first opportunity (after researching any live alien IIRC). Hit the live and autopsy versions of Eggs, Multiworms, Hyperworms, and Chrysallises before moving on to other aliens. To get hyperworms just kill a multi from far away and then drop stun grenades in a wide area around them. Avoid killing multiworms close up as the offending agent isn't likely to suffer the resulting acid shower from these nasty little things.
The advantage of having three physics labs is that you can research all three alien ship components at once so you can get to the X-Com ships sooner and you'll quickly be able to identify less useful early alien weapons so you can sell them for a lot of cash. Be sure and research at least one of the components as soon as they become available since this will give you access to the advanced physics lab research. Once you start researching useful stuff in an advanced lab, you can still do UFO research and research any trinkets you have with the smaller ones.

General Strategy

Watch the allien ships carefully. At first, they will only send one class of transporter and one class of escort ship that drops aliens into buildings (you can see a little energy column when transporter ships stop to hover over a building). Of the first wave ships, the round ones are the transporters and the weird ovoid ones are the defenders. Try to take out two of the transporters before they drop aliens off so you don't have to clear three seperate buildings out. You'll want them to drop in at least one place so you can get your hands on some of the earlier tech. In medium difficulty, the aliens will only occupy one building when dropped from the smallest ships. I think in harder difficulties they'll occupy surrounding buildings even if you investigate immediately after a dropoff. All larger transports will tend to drop aliens in more than one building, so after you've investigated the one you know they dropped in, save the game and hit all nearby buildings just in case. You can reload to avoid needlessy pissing of the corporations
Once the larger ships show up, you can get all the tech you need from the shot down UFOs themselves since you actually have to kill all the survivors to recover them. For this reason, you should try to waste the transports before they get a chance to drop aliens off since it will likely mean multiple missions where you have to worry about property and civilians. I've had games where I did a lot of tweaking, saving and reloading. If you consistently prevent them from dropping aliens off and take out the majority of their ships, it will seriously slow the aliens down giving you time to get a leg up on bioweapons research.
The first manned UFOs that show up are the Transporter and the Fast Attack ship and in my games they tend to hit in the second week. The fast attackers can be deadly but taking one down early on can be a coup since they have Medium Disrupters which will give your Hawk Air Warriors the power you need to start dominating the aliens. The light disrupters for vehicles are kind of like the first personal disrupter. Nice for low ammo cost but not as good as Earth tech for damage. Once the aliens show up with shields, research this ASAP. With these, the Air Warriors can actually hold off just about anything if you stack a couple of them.
In the first week you should be able to get by just fine with hovercars, but I recommend raiding the cultists to get enough jink to buy every Hawk Air Warrior you can as the weeks go by. Don't buy more interceptors, in fact I tend to sell the first one I have so I can get better stuff in a lot of games. They don't have more firepower than air cars and they cost almost as much as the warriors. Once the bigger ships show up, I tend to phase the interceptor, cars, and any bikes I have out in favor of air warriors. Nothing else can handle the punishment that the Fast Attack ships dish out.
To take those transports out before they get a chance to land troops, park your vehicles in non X-Com buildings between alien attacks so that you can spread them out a bit more and always have some ships close to the action. Put each one in a seperate building so they can all take off faster.

My opinion on weapons:

Lawpistol - Short of putting on an agent as backup in case they run out of ammo for a launcher of some sort, I nevere saw a use for these. Mighty cool looking though.

Autocannon - These guys punch through armor nicely, but they have the same heavy weight, crappy accuracy/low ammo issues of the past. The explosive and incendiary rounds tend do more damage to the stuff I want to keep around than the enemies themselves, so I skip these. Careful with fire and explosives. It will set off ammo and destroy gear on the ground and that can hurt your profit/research options. I tend to watch the reaction fire of cultists with these a bit more carefully since even one shot can punch through Megapol armor and cause injury.

Incendiaries of all kinds - Fun but not practical if you want to preserve gear for tech and profit. Also, lighting things on fire can block your vision and make corridors impassable. I don't use them.

Marsec M4000 - Most consistently underrated weapon in all the strategy guides I've ever seen. The rate of fire on these things is insane. Accuracy is lousy and they don't penetrate armor without a lot of shots, but early on in the game shots at full auto only cost 1 TU. If you place your troops in positions where enemies are likely to come around corners the ROF really kicks in. I've seen guys get like 15 shots in reaction fire before. At close range, the Marsec is murder. I'll frequently run an agent right up to 2-3 enemies and just have him hose them all down with lead. Even if they have some TUs left for reaction fire, they're frequently dead before they get a chance to fire a single shot (you can see them raise their arm to shoot but never get a shot off). When fighting armored enemies the bullets will get blocked at first but they deplete armor rapidly. A good backup against brainsuckers is to keep one man at full auto close behind an exposed agent. I give all my guys Marsecs at the start of the game.

Laser Sniper Rifle - No power, lousy penetration in my experience, and takes too much time to fire. I was psyched when I first saw these things but they're not worth it, IMO. Cultists with these are probably the most negligible threat in the game. Maybe they're good for zapping poppers safely, but I prefer finding and blowing poppers while they're still next to their buddies.

Plasma - These are pretty nice if you want to play a more traditional game of X-Com where reaction fire and spotting enemies with one agent and shooting them with another that the enemy can't see (and consequently can't shoot back at) is your preferred strategy. They also cut through armor a lot faster than the Marsec does. Also, I think energy based weapons are less likely to cause poppers to explode. Not sure if this is the case with plasma, but when you hit them with alien disrupters they never seem to explode. I still find the Marsec to be more fun and effective in the early game though, since your agents tend to have lousy aim at first anyway.

Stun Grenades - Always buy every stun grenade available and never sell the ones you get from the cultists. These things are the secret weapon of Apocalypse. Normal grenades simply aren't powerful enough to kill quickly whereas stun grenades can drop 8 cultists if they're packed into a room, do no collateral damage, and can be dropped at key choke points to take out a lot of enemies. I wiped out all but 2 of an entire crew of aliens on the first Fast Attack Ship I took out the other night by throwing one of these up to the second level. All that was left was a half conscious anthropod and a spitter panicking upstairs. All the rest ran right into the cloud to try and get to my guys and it was over. They're also essential for multiworms, since you generally want to avoid killing those guys, especially if you're a close range Marsec assassin player like myself. Just dose the worms and pump them full of lead on the next round.

Regular Grenades - Great for splatting Brain Suckers and setting off poppers. These are my preferred weapon of choice for long range attacks early in the game since the Marsec can't hit the broad side of a mother ship from 5 squares away. I also use loads of these on clusters of enemies when I don't think I'll need to waste a stun grenade on them.

Proximity Mine - Not quite the super weapon they were in the original X-Com but they still have their uses for blocking of corridors and do considerably more damage than regular grenades for tougher enemies. Enemies almost always move when you've been spotted so you're guaranteed these will go off next turn if dropped at an enemy's feet. They're also handy when you suspect a popper will be coming through a choke point.

High Explosives - Haven't messed with these much. They seem too heavy to me, but I'll have to give 'em a closer look.

Smoke Grenades - Once every five hundred battles or so, I wished I'd held onto these, but if you play the game right you'll almost never wish you had one. Still, they can be handy for blinding that popper long enough to get an agent to safety.

Plasma Sword - You'll probably already have your hands on Devastator Cannons by the time you get enough of these to equip on all your agents, but they pack quite a mean punch and will cut through most walls for convenient shortcuts. If you've been using Marsecs well, the same close range strategies apply.

Disruptor Gun - It took me a while to realize just how bad these things suck. The only advantage is no ammo consumption. Stockpile these and sell them for a nice profit, but I'd rather stick with Earth gear than use these. They have lousy accuracy don't actually do all that much damage and take way too long to shoot.

Devastator Cannon - These are very nice, although usually short lived since I typically have Level B Toxiguns on the back burner by the time I get enough of them to equip everybody. They punch through walls like nobody's business and are more accurate than most weapons. Once you get these, you won't have to get in close anymore.

Toxigun - This is the ultimate alien killer until you get gas. It doesn't take long to get to level B clips so I usually wait for these before I start using them. Very accurate for a pistol, deadlier than the Devastator Cannon, and they shoot about as fast as the Marsec. The only disadvantage is that they can't punch through obstacles. The huge advantage is that they don't hurt humans in the event of friendly fire. Hold on to those cannons for the cultists, but these should be your permanent upgrade for taking out the aliens. You can work on getting these things ASAP the second you start capturing live aliens.

Heavy Launcher - These things do catastrophic amounts of collateral damage and while the blast radius will tend to evaporate all gear on the ground it seems to lose a lot of punch against enemies farther out. Since you don't want to be blowing the crap out of places you're protecting, and you don't want to be vaporizing all that psiclone on cultist raids, it really only comes in handy when defending your base or raiding alilen ships. I generally find that these things are more trouble than their worth. When I see cultists walking around with these I prefer to stun grenade them rather than risk a close range reaction shot.

Mini Launcher - Much less damage, same issues. I never bothered with these.

Vortex Launcher - This actually will kill large cluster of softer aliens, but the collateral damage issue is even worse. I usually only use these on particularly large UFOs, the alien dimension, or when I have plenty of money and want to have some fun with the cultists.

Boomeroid - More trouble than they're worth, IMO. They don't do a ton of damage and if you're not careful, you'll find them running down your own guys.

Vortex Mine - The ultimate grenade. I still keep stuns on all my guys for preemptive purposes and bypassing shields but I think these things have the most powerful explosion in the game for the purpose of destroying structures, and they can be extremely potent against tightly packed aliens. They're also the best weapon for destroying those orange floor panel gates that aliens get reinforcements through in the alien dimension.

Gas weapons - You can get gas weapons if you capture the alien queen and research her, so this is only a late game weapon but this is where you'll want to pull out those Heavy Launchers since the gas basically works about as well as stun grenades on cultists, only it kills all aliens outright and the Heavy Launcher version will create a huge cloud of the stuff, giving you massive visual cover while elimating anything that tries to come near. This stuff is even bettter than the Toxigun and once again, totally safe for humans.

Vehicle Weapons:

Lasers and Guns - Forget about it. Missiles and plasma are way better. If you don't believe me, watch the cops try to kill gangsters with these. It's pathetic. If money is in short supply the heavier lasers work decent on the first week but after that try to upgrade.

Janitor Missiles - These launchers are nice because they hold a ton of missiles. They work fine for the first week and I recommend using them exclusively until tougher ships start showing up since you start out with so much ammo for them.

Prophet Missiles - Much lower ammo capacity and only slightly more power than Janitors, but they get a nice range boost. If you're going to use bikes after the second week, this isn't a bad choice since they can stay farther back. Make sure you set the bikes to defensive. They'll die fast otherwise.

Rendor Plasma - Buy these and all elerium every chance you get. You won't need them for the first week, so don't waste the elerium, but they're nice to have on your air warriors once the bigger ships start to show up.

Plasma Multisystem - A great choice for the front slot of air warriors until better weapons become available. Their ROF dishes out damage faster than the Rendors and they keep firing even when you're not directly facing an alien ship to keep the heat on while turning.

Lineage Plasma - Until you have enough new X-Com ships, you'll want to buy these for all your air warriors since they can't fit alien weapons on the wing slots. These are a drastic improvement over the Rendor and will go a long way in taking out those first big ships.

The Heavy Missiles - I haven't really messed with these. The stats on them don't seem to impressive although I think the smaller ones might fit on hoverbikes which could make for a handy swarm strategy in a pinch since the range is so extreme. since the ammo cap is only 1 their potential damage is pretty lousy compared to most weapons, but might be worth it for cheap bike geurilla tactics. I don't the larger missiles will even fit on the hover cars so I don't know what the heck you would use those for.

Weapons Control - I buy these at every opportunity since they are always in short supply. I'm not sure if they help missiles at all but they definitely have a noticeable effect on beam weapons. You still miss the faster ships a lot but there are fewer stray shots leading to nasty collateral damage.

Light Disrupter - Look at the damage and the ROF. It's really not a very powerful weapon.

Medium Disrupter - This is the first alien weapon worth using and completely outclasses anything else you could but in the Hawk Air Warrior's front slot.

Heavy Disrupters - They only fit on Avengers but these things are incredible.

Alien Missiles - If you've got some brilliant financial scheme for affording all the ammo, I recommend not using these at all. Avengers with nothing but disrupters do just fine. The stasis missiles can be cool but are also very expensive, whereas a well armed and shielded Avenger can handle most situations with ease. Be extremely wary of alien ships that shoot stasis missiles though.

Dohickeys:

Motion Detector - I like giving these to all my agents for tracking down stragglers or just getting a good idea of where aliens are camped out on ship recovery missions.

Personal and Vehicle Shields - Having more than one of these on a unit will cause them to stack, and yes, personal shields work even when inside your backpack. Stun grenades are a great way to load up on extra shields and the Toxigun goes straight through them IIRC.

Personal Stealth Field - Use it. Even if you're using two handed weapons it's worth the tradeoff in accuracy since it will drastically reduce alien accuracy in a much bigger way. If I had to pick between these and shields, I'd pick these if I didn't like the fact that doubled up shields allowed me to be so careless with my men. If you're a careful player the Stealth Field is probably one of the most powerful items in the game.

Teleporter - Not a great item in turn based. I saw a FAQ saying you can get these things by researching shield tech. The only way I ever got them was by taking them from the aliens in the very last alien dimension mission and retreating to research them. Fun for playing pranks on the cultists but I don't think it would be that great since it takes so many TUs to use anyway.

Psionics - Psionics are weak against so many aliens in this game and they're so much more limited than in previous games, I don't really bother with them, although I haven't tried a team really focused on psi use yet.

Eh... oops. I guess that wasn't a short post was it?