Oooo, I would command the Serenity. And my first official act would be to make ex-Captain TightPants my First Mate. Or my sex slave. Tomayto, tomahto.
And that chick on my shuttle has to go. Now.
Pilot? I’m in command… let somebody else do that. I’m busy counting my doubloons.
The USS Discovery from 2001
Almost as pretty as the Enterprise-A and, since it is made with turn of the millenium tech, much easier to maintain and repair.
HAL tells me the antenna thingy unit should be allowed to fail before replacing it with the spare, I say " Yeah, okay. Sure!" 
“Slapstick” Libby? Is that Slipstick’s circus clown brother?
Sheesh, why do all you people want huge crews to manage? Talk about headaches. I want something that can be run either by myself, or by a small crew (no more than four), or by a single sane AI. Something with a bit of living space (not all that much needed, just enough.) and SSTO capability, preferably with some kind of star drive as well.
Which leaves me the following vessels, I think: Gay Deciever, a T.A.R.D.I.S., or Ryo-ohki from Tenchi Muyo.
Dahak might squeek in there, except that the idea of landing him anywhere is kinda dangerous.
That’s what the sublight parasites are for. Besides, Gay is just too small, and if I were cooped up with the same people 24/7, there would be mutiny or beaching within a week. No, give me a huge ship to command, so I have a plentiful supply of redshirts to do the dangerous stuff.
I know Gay is small - that’s why it would be just me and her. And Barsoom is just a hop, skip and a jump away, if I need to walk about.
You need to paint it pink, or some other unexpected color that is inexplicable or unexpected.
Stranger
I’d like to have the big chair of the SDF-1 Macross. Whether UN Spacey or RDF, that baby is one of my favourite starships ever.
How about the Teacher? With Gay as the shuttlecraft, of course.
There would be a advantage of having two different drive techs…
That’s why I broke out the two categories.
USS Reliant NCC-1864-B, a Genesis-alloy clone of the original mined out of an asteroid from the explosion of that planet.
Well really as long as it makes it to ludicrous speed , its all good.
Declan
Command: USS Excelsior or Enterprise-B - I always thought the Excelsior class was the most elegant looking.
Pilot: X-wing - I’d much rather be a Star Wars fighter jock than a Star Trek helmsman (unless I could get Worf’s ‘little ship’.
Yes, and every time there’s a major breakdown, you, as captain, are entitled to spank the ship’s mechanic.
Any other questions?
s’ok the defiant was in a movie. It was plot crutch A to get Worf on to the Enterprise.
I sit duly chastised and corrected. I hadn’t thought it through as completely as you. Excuse me while I find a place to hide this toolbox.
Command: I’ve always liked the way the Reliant looked, so I’d go with it.
Pilot: Koensayr BTL-S3 Y-Wing.
Jefferson Starship!
Trying to not be a jerk, but what’s the difference between all those Star Trek ships? They all look the same to me.
Size, degree of streamlining, and arrangement of warp nacelles, I’d say. Roddenberry once suggested that all Starfleet warp-capable ships should have nacelles (in multiples of two) symmetrically arranged outside of a primary hull, perhaps in reaction to the popularity of Franz Joseph’s Star Trek Technical Manual, which had some one- and three-nacelled starships. But later ST production teams modified (or ignored) Roddenberry’s precepts, so more recently there have been some very offbeat designs.
Here’s a good article on the subject: Ex Astris Scientia - Starship Design Guidelines