namely, my suggestion would be:
DB server -- NSEA Protector (Galaxy Quest)*
because the movie plays with reality, being a fan and how fiction and reality can merge to form something kick-ass (By Grapthar's Hammer!)
Rails1 -- Millenium Falcon (Star Wars)
Rails2 -- Serenity (Firefly/Serenity)
because they're both speedy and strong!
Original #1 -- Enterprise (Star Trek)
because, no matter the letters after the name or the universe, it's always the Enterprise
Original #2 -- Galactica (Battlestar Galactica)
#2 because there are two Galacticas - the 1978 and the 2003 one
Storage -- Heart of Gold (Hitchhiker's Guide)
because fandom absolutely has that heart of gold, and because it is ripe with infinite probabilities (which is kind of close to the drive system of the Heart of Gold, if slightly different...)
Switch -- TARDIS (Doctor Who)
not technically a spaceship, I know, but it makes switching between places and times possible, so...
* I was going to suggest Nostromo (from Alien) for the DB server, but after having read up on the origin and meaning of the name, uh, maybe not so much
because its main computer is called MU/TH/UR (mother) and because