USS Intrepid, name ship of the Intrepid-class.
Why? It's small - small enough for me to detail every single NPC on the ship (well - at least name, rank, species gender and key skills; and yes *sigh*, I am that anally retentive
); there's a tonne of source material out about it; I've got the really cool cutaway poster of Voyager; I'm somewhere in the midst of deckplans for it (though I keep having to go back and revise decks...grrr!).
Story reasons are that it's the smallest multimission ship I can think of. Nova is great for science missions, but it falls down when I want to do first contact or combat-oriented stuff, Defiant is good for combat stuff, but falls over regarding exploration stuff.
How's it working out? Terrific!
When you are dead, you don't know that you are dead. It is difficult only for others.
It's the same when you are stupid...