An easier mechanic to implement, over seperate logistics points for "carrier" hulls, would be just to implement a "fighter bay" ship module that would function similar to a standard weapon mount. You'd have your three weapon choices, and the fighters would otherwise be unshielded/unarmored (you gotta figure they're too small to carry much more than short-range engines and a single weapon of choice) and completely dependant on the carrier's survival for their own survival.
Hence in combat, the carrier itself would show up, but it would "fire" its fighters at the enemy ships once, or until a fighter is destroyed (and another is launched to take its place), but instead of the fighters impacting against the hull like normal weapons, they simply stay animated as pseudo-ships in the battle, each adding their firepower per turn as if the carrier itself were given multiple attacks per turn (one for each launched fighter, in addition to combining whatever standard weapons are mounted on its hull as one shot like normal).
Heck, they could even adapt such a system to accommodate disabling of enemy weapons, shields, etc during a prolonged battle to add further depth to the system, as it makes little sense that a ship with one hitpoint out of 80 left can still fire its weapons and power its shields and engines as if nothing else was wrong with it.