Constitution-class. It was sleek, it was new for the time, and it wasn't a luxury liner cruise ship that was randomly inconvenienced in space. Didn't Galaxy-class ships have multiple gyms and then the arboretum? Too many children for my liking as well.
Romulan D'Deridex-class Warbird or Vor'Cha class Klingon attack cruiser?
Captain Picard, by far. Kirk was swashbuckling but entertaining, Janeway was entertaining and principled but broke lots of ethical rules for me (lots of Prime and Temporal violations; biased interpretations of intervening, Equinox, etc.), and Sisko...eh, I just don't think the role of a strong Captain really ever appeared necessary or materialized for Deep Space Nine, since it was a space station, Bajor was nearby along with the Bajoran Wormhole, they had the Defiant, etc. It would have been "cheap" to give DS9 and super-strong captain and a Galaxy-class starship, for example, especially given the refit. Archer was okay but ENT is easily my least favorite.
I consider myself to be half-Vulcan, half-Betazoid in a Trek universe, but when considering ships and culture, Klingons win. What I wouldn't do to command and pilot a Negh'Var with a group of Vor'Chas behind it. The losers are Romulans. I adore the D'Deridex-class and Scimitar-class Warbirds immensely, but Romulans themselves are "so predictably treacherous!"
Data! Lore was just kind of creepy and poorly-executed anyway, and I never liked him. His teaming up with the Borg or the Crystalline Entity never made sense either way. Data's also one of my favorite characters in the franchise anyway.
Voyager had better individual episodes with a lot of misses, but DS9 did arcs better. Gah. In theory, Voyager, since I like the story and the Borg more. I think DS9 executed better and I like the arcs it did. I don't know how Voyager got away with not doing them.