Here is a little advice on the very early game - i.e. before you have discovered laser rifles and produced them. You usually get a terror site and several ships before that point, even if you research really aggressively, and if you try to take on them using projectile rifles as your main weapons, you're gonna be up for a disappointment.
So, here's how. Forget rifles - take pistols instead. Pistols are about as good as rifles if you use snap shots, but they let you hold a grenade in your free hand. Grenades are great early on because most aliens die if you toss it anywhere near them, which most rookies can do with no problems.
Also, take rocket tanks - they are incredible machines, especially when you are out in the country with no civvies but still quite a few obstacles and buildings. Why go into a building when you can blow out its wall?
Advance with tanks - they have the armor to oftentimes take a shot from the heavy plasma even and survive, which is more than you can say for your rookies. As soon as the tank spots an alien, have the three soldiers that are trailing it fire at it. Doesn't matter if they can't see it, they'll still have the same accuracy.
Use 2 tanks and 6 soldiers, and you'll have two teams of armor+troops. With it you can usually take out an early terror site or downed ship pretty easily.