Light Fighter: Hawk (Gecko)
Heavy Fighter: Chameleon (Stiletto/Paladin)
Very Heavy Fighter: Anaconda (Titan/Crusader/Defender)
Fighter/Bomber: Vulture
Bomber: Panther (Mamoru)
Freighter: Clydesdale (Draugr)
Transport: Serenity
Gunboat: Claymore (Defiant)
Frigate: Raba
Cruiser: Caliburn (Archer/Thresher)
Battlecruiser: Togo
Battleship: Murmillo
A little bit of an obvious bias in there. Many of these are also my most used/comfortable ships in the given class, though BC and BS are based purely on looks as I never fly those. I added honourable mentions in parentheses, picking just one was a bit difficult.