Aldran Adventurer: Terran Springblossom (M6)
Anonymous Argon: Argon Elite (M4)
Argon Anarchist: Argon Nova Vanguard (M3)
Argon Patriot: Argon Nova Vanguard (M3)
ATF Veteran: ATF Thor (M3)
Bankrupt Assassin: Pirate Mamba Raider (M3)
Boring Boron: Boron Octopus Explorer (M5)
Cunning Charlatan: Terran Xperimental Shuttle (M3)
Goner Witness: Goner Truelight Seeker (M6)
Humble Merchant: Argon Mercury Hauler (TS)
Hunted Hero: ATF Verdandi (M3)
Formidable Freebooter: Pirate Carrack (M7)
Lost Lar: Boron Angel (TP)
Nostalgic Argon: Argon Buster (M4)
OTAS Operative: OTAS Sirokos (M6)
Paranid Prospector: Paranid Demeter Miner (TS)
Pious Paranid: Paranid Demeter (TS)
Poisoned Paranid: Paranid Demeter Hauler (TS)
Savage Split: Split Asp (M4)
Surreptitious Smuggler: Split Iguana Vanguard (TP)
Teladi Trafficker: Teladi Vulture (TS)
Terran Defender: Terran Sabre (M4)
Terran Tourist: Teladi Vulture Super Freighter (TS)
Tormented Teladi: Teladi Harrier Explorer (M5)
Unholy Traitor: Paranid Medusa Prototype (M3)
USC Commander: Terran Excalibur (M3)
Xenon Rogue: Xenon PX (M6)
Yaki Insurgent: Yaki Susanowa Raider (M3)
Yaki Ronin: Yaki Appallox (M6)
Advanced Start: ATF Vidar (M6)

These are only the player ships when you start a new game. A few of them have additional ships owned by you.