1) Tough pick between the Argonev and Transcendia. Argonev edges out on looks.
2) Obviously, the Orkulus is the best for offense since it moves, and deals extra damage against buildings. It doesn't have abilities that screw with masses of ships, but it can keep itself alive either with the deflector shield, or debris-suck-repair. This helps it on the defense as well, but I think the Transcendia is a bit better at it. It can hit the entire enemy fleet with the meteor, which is a pretty frequent cast and deals good damage. It also has an ability that disables all engines/movement of a group of ships and has a very long reach, so it can hold a bunch of ships out of their normal firing range but within the starbase's. That also screws with anything that requires direct facing, since the ships just kinda twirl around with disabled engines. The Argonev wins best support, since it can build ships and provide repairs (and I think AM?) to nearby ships.
3) For pure firepower, the Orkulus with its third weapons upgrade that grants it +30% damage. It also has the highest base hull and shield hp because it has 4 structure upgrades, but between the 3 weapon and 4 of those, it only has one slot free for utility, which leaves it more limited in that regard. By contrast, the Transcendia can max out weapons, armor, meteor, and get a rank of mass disorient.
Of course, these are just my opinions, I'm not stating them as fact (except 3), in any case) 
