Capitals include Orions, Deimos, Aeolus, Fenris. I do not remember them fielding too many Leviathans, if any at all. It should be noted that Fenrises would likely be a lot more common based on cost and speed as NTF fights guerrilla largely.
Fighters would most commonly be the old Hercs, Ulysses and Lokis. They have fielded more "advanced" ones such as Herc.II and Myrmidon but that is about it.
Bomber-wise Zeus and Medusas.
Other ships I would NOT expect them to field includes Charybdis and Triton, nor would I expect them to have any Mjolnirs to field. Would be a fair guess that they will not have the Zephyrus miner either as it was developed later and the NTF as a whole had little business with the nebulae.
About the Perseus, one or some of those multiplayer allows you to fly it as the NTF. However, by canon I would say they do not have it because it is still largely a new design, and even if The Sixth Wonder was not the first fielding of the ship I would not expect NTF to have the schematics.