[Noble713]

Attack Ship:
Mixture of Meson BLasters and Capital Missiles (until good Plasma Missiles are available), moderate to heavy shields, no armor, and 1 point defense. Maximum speed usually 6, and combat sensors. ECM only used on cruisers.

Planet Bomber:
Replaces my combat ship's meson bLasters and missiles with Planetary Napalm. Napalm replaced with neutron bombs when available.

Fleet Train: (just started using it today)
Cruiser size, light shields, 3 solar collectors, 2 repair bays, 1 mine sweeper, 6 engines. The rest is filled with supply storage. At max tech, that's 6000 supply points, or about twice that of any other ship.

Transport:
Nothing special here, just a transport with lots of cargo for troops and some extra supply.

Builder:
A cruiser with a space yard. Space yards are so big you can't put much else on the ship. I only use these for building asteroid mining space stations, and on rare occasions, warp point defense stations.

I've also gotten into the habit of putting colony modules on medium transports. They are far larger than Colony Ships, and can drop far more people on a new colony.

I've tried using a carrier-dominated fleet, but as you said fighters are too slow and it doesn't take the AI long to put PD on its ships and run away from your fighters, shooting them down as they try to close the range.