Excelsior. I'd put those AA batteries back wherever Scotty took them out and try that transwarp drive for real!
Oberth. That way I'd get the mundane assignments and be relatively safe. Of course, the few times we've seen the Oberth class has involved catastrophic failure in one way or another, so at least I'll go out with a bang.
Galaxy class definitely, best at everything. Next would be the Nebula, Excelsior, Ambassador, Sovereign, Intrepid, Akira. Last would be Defiant, worst at everything.
Since I have a science / research background in RL, I would choose a Nova Class and go on specialist research missions preferably stellar cartography and exogeology. I'd take a good medical team too, given you never know what sort of critters and microbes are out there on uncharted, far-flung worlds.
I may have been the only to make this vote but...Nebula-class. I love the look of the ship. Seems like an edgier Galaxy-class.
From 'canon' Trek, circa the 24th century, the Galaxy class. No question. Looks a truly magnificent vessel to voyage space in, as (re)watching TNG series 3 is currently reminding me. If not the Galaxy, whatever class of vessel succeeds it. No, not the ugly, grim warship type in First Contact, but a real exploration starship.
I think from Star Trek online the Odyssey class is the true replacement for the Galaxy, although not strictly "canon" it's an interesting design. I can't remember where I read it but I'm sure the Sovereign was meant to be the replacement for the Excelsior class.
Almost impossible for me to answer. I love so many of those designs, and small or large would depend on the type of missions I'd do... I can't decide !
The Galaxy class, with its varied sensor arrays, comfortable quarters, and beautiful design, is the ultimate starship of scientific exploration for me. It's a close call, though, because I prefer the Constitution class bridge layout. Its hub-and-spoke design seems better for communicating information to the captain, especially from the science station.
Prometheus class because I'm a Voltron fan. If not that the Abrams Enterprise, NX or Sovereign in that order.
I really like the Intrepid class. But for me, it would be a training ship, so I could still be a teacher, and have a relatively safe assignment. I want to come home and who are we kidding? I'm no James T. Kirk!