Laser turrets are good all-round, with fast fire rate, small damage and high range.
Flak turrets fire slow at close ranges, with high damage; they are good against fighters, asteroids and mines.
Rocket turrets fire very slow, but have high damage and medium range; they are good against capital ships, but they may also prove lethal against fighters.
The repair bay produces drones, that orbit your ship and repair its systems. Make sure to constantly upgrade it. Also make sure to check on your turrets health a lot and repair them manually in the Build&Upgrades section.
Fighters are good to draw the enemy fire away from your carrier. Build more fighters bays and upgrade them to make them more efficient.
Selling a turret gives you back 80% of its RU value (including the upgrades).
Capital ships turrets (including yours!) can be destroyed by firing in their vicinity. Make sure to upgrade the hit-points of the turrets near the edges.
Difficulty levels offer different gameplay experience. While nothing will go wrong on easy, things change dramatically on hard difficulty.
The common (but not the only!) strategy for the hard mode involves selling the fighter bay in the beginning as the
enemies will be driven directly to your carrier, making them an easy kill for the ultragun. Then alternatively upgrade the ultragun damage/fire rate and the drones count/repair. After level 3, you'll have RU to invest in a couple of laser turrets, 4 or 5 would be enough. Choose the top/tower hardpoint, 2 or 3 in the ship center and one at the bottom, near the ultragun, this way they will cover multiple incoming enemies vectors. Upgrade the turrets damage and fire-rate, and for the one near the edges, upgrade one level of the hit-points. It's possible that for the last chapter, you'll need to sell the laser turrets and invest in a couple of fighters, to draw away the massive damage of the boss and its minons.
A video walkthrough of this strategy is available here (thanks to whoever made this!)