Turks Island fort is relatively small, and once you land troops, there aren't many fighting scenes before you get to the governor. You can see from the screenshot how much money I got from him. Alternatively, first go in under a false flag, visit the tavern and recruit a couple of drunk officers. Then go back to the ship, hoist a hostile flag, invade, and put those drunks in charge. Now you get a small but steady income from taxes, and you can rename the town if you like.
By the time I have a ship capable of taking on a fort, I already have plenty of armour and equipment. This is because I don't give myself a battlewagon at the start of the game, I get it second-hand, so to speak. And I don't even try to board a warship until my officers and I all have at least battle armour, preferably gold armour, plus good swords, and the boarding crew also has battle armour plus decent swords. If we're capable of taking a Soleil Royal, or even a 3rd rate battleship, then we're easily capable of slicing our way through a fort's garrison. Weapons are also taken from dead enemies - captured ships, dungeons and the many highwaymen are all sources of free weapons. But I do buy armour - for some reason, Spanish ports seem to be better stocked with battle armour and gold armour than anyone else, and San Juan has several street traders.
And so the biggest challenge is the initial bombardment. Martinique is easy, you approach from the north and you're screened by a big rock until you're close enough to the fort to bombard it. Guadeloupe is tough, it has two forts and one of them is hidden behind a couple of big rocks so it's hard to hit. But if you want a real challenge, try Cartagena. It's on a peninsula and it's a large fort, so half the guns are out of range of your cannons. So you have to bombard it from one side, wipe out all the guns you can hit, then sail round to the other side and finish off the rest.