Carrier - Armitage (can equip cannons and has a nice turn rate)
Cruiser - Chel (ditto)
Science/Multi-use - Fleet MVAM/Mobius/Korath (gravity well + turn rate + cannons)
Escort - JHAS (5 tac consoles + BoP turnrate + non-BoP HP)
I care a lot about turn rate because turning is the most annoying aspect of space combat. I tried a Jem Dreadnaught once (turn: 6) just to check out the fighters, but after a few battles, I honestly don't know how anyone can stand to play any ship with a single-digit turn rate.
I keep coming back to the Breen Battle Cruiser... 8 weapons slots, +5 all power systems, Hull and turn rate, it works for my Trill Engineer and my Klingon tac officer.
I want the Breen BOFF layout in a Federation starship.
Multi-Vector Advanced Escort is almost identical except is has an ensign tac instead of an ensign engi.
Best Carrier: Kar'fi
Best Battlecruiser: Fleet Tor'Kaht
Best Raptor: Mirror Qin (not much choice here)
Best Raider: Fleet B'rel
Best Small Craft: Um... who cares?
Best Destroyer: Breen Chel'Gret (yes people, it's a destroyer, NOT a cruiser, NOT a battlecruiser)
Best Cruiser: Fleet Assault Cruiser Refit
Best Science Ship: Fleet Reconnaissance Science Vessel (even though when it comes to science ships, it's really users choice since each one does different things)
Best Escort: Jem'hadar Attack Ship
Best Escort Carrier: Fleet Armitage Heavy Escort Carrier