In order to be offered carronades (and special figureheads like a goddess), doesn't your luck have to be pretty high? At least that's my experience. Luck can be influenced by donations to the church. Only the percentage of your money you donate counts, not the actual amount of money. Therefore, load your ships with something valuable (gold for example), so your cash is really low. In the end you'll have donated really small amounts of money to get the same rise in good fortune.
Fortune tellers can give you an idea of how lucky you are at the moment (sounds logical
)
Tekkousens are faster than full-rigged ships. That's why I prefer tekk's for trading, while full-rigged are the ultimate choice to build a battle fleet.
While the Athens-Istanbul is the best short route to make a good profit, unbalancing trade routes like Madeira - Genoa or Madeira - ?? (either in Northern Germany or in Denmark; this port gives you silver, forgot its name, it might have been Lübeck, this port pays most for gold) is a lot more profitable. I got this idea from an FAQ I once read, so I don't claim any originality.
It works like this: by selling and buying small amounts at a time, you can rise or lower a port's price level at will (between 50 and 150%). Buy gold at 50% in some African port, then travel to Europe and sell it at 150%. It's a little tedious to buy or sell small amounts so many times in a row (to influence the price level), but you can make several millions in one haul this way. You have to start with quite some capital though, for example when you've worn out the Athens-Istanbul route.
Also, don't forget appointing a good book keeper, he'll be able to give you considerable discounts when you're buying goods and ships. Never agree on the price a trader or ship builder is proposing. However, it has to be a GOOD book keeper (with accounting skills): if you offer a ship builder too little, he'll kick you out, and it takes a while before you can buy ships there again.
A final tip (probably only useful for starting players, it's not like I'm telling something miraculous here): if you can get your hands on some of the best weapons and armor in the game, and your character is good at fighting, picking a duel with the enemy captain can be the fastest and cheapest way to win a battle. However, don't try this with weapons that are just good, you'll better get some that are rare (in other words, that you'll only find between 2 and 2.40 am in one particular port). Read which weapon is good for which type of attack, so you can deal the most damage during battle. Sounds stupidly simple, but it's so easy to ignore the weapon info you get when buying it