I'm going to be more open on choices, as I would have a tough time choosing. I will pick two to three ships, one from each species/government, for TOS, TMP, and TNG. I won't bother with Pre-TOS, as I'm sure non-canon designs are unallowed and even if they aren't, it'd give me a harder time choosing.
To make sure the topic starts out open,
TOS Starfleet: No contest: The Constitution-class. Aside from the Enterprise, if I was given command of one, it'd be the non-canon NCC-1716 U.S.S. Endeavour.
TOS Alien #1: Tholian ship. Add a little paint job, crystalize it a bit more, and give the species some more variance, I'd definately be intrigued by this species. The design may be simple, but I like it.
TOS Alien #2: Because combat isn't totally-realistic, I say the D7. Efficient warp drive systems, disruptors, and built for battle, an efficient battlecruiser that was made to rival the Constitution-class, I guess. Or was it vice versa?
TMP Starfleet: It's a real tough choice... I certainly would rule out the pathetic-excuse for a refit for the Enterprise-B: As the huge impulse engines would've actually melted off the pylons. I prefered the original streamlined Japanese-esque design of the Excelsior-class, yet with the minor refit touches seen in Star Trek VI. However, the beauty of the Constitution-class's refit rivals the Excelsior's own distinct beauty. Probably the Excelsior-class, a more-modern design proved efficient since 2285, and whether hauling butts between Starbases in the mid-2360s or vaporizing bugs in the Dominion War in the mid-2370s, it is a formidable 90-year-old design. I might choose this, but I definately wouldn't forget the beautiful Constitution-class refit. My decision between those two ships aren't final, though.
TMP Alien #1: K'T'inga-class Klingon Battlecruiser, successor to the D7 class, and the first bunch of ships we see digitized into data patterns for V'Ger's knowledge in Star Trek: The Motion Picture.
TMP Alien #2: V'Ger. One of the most-powerful ships in the known galaxy, let-alone universe, it can produce an energy cloud up-to 2 AUs in diameter (or 82 AUs in diameter, if you prefer the original cut) and digitize just about most any ship it encounters. That character shielding is an exception, which is exactly why the Enterprise survived (unless they sent the Hood for assistance or whatever other ship the original script called for). TMP is an under-appreciated movie that's actually mostly Gene Roddenberry-influenced right down to the uniforms. But then again, I'm all for unique tastes that are minor. But don't let the Borg come near this thing, or it'll be digitized into data patterns until they're extinct!
TNG Starfleet: A tough choice: Many good selections. I'd have to say the Galaxy-class Starship. The one, the original TNG Starfleet design Probert made that defined the look of TNG starships (until Eaves started going for cool looks and ratings instead of prefering design lineages). An under-appreciated design, like the Ambassador-class I would guess, a very-good design in itself that derived from one of Probert's original sketches of the Enterprise-D.
TNG Alien #1: The all-too-beautiful-yet-all-too-menacing Romulan D'deridex-class "B-type" Romulan Warbird, a Warbird bigger and better than the Galaxy-class, and perhaps the Sovereign-class as well! Or so in my opinion. A beautiful design nonetheless.
TNG Alien #2: Vor'cha-class. The first true Klingon design that also defined TNG ships for the Klingons. A design that borrowed from the K'T'inga and D7-class starships, a ruggedly-beautiful yet built-for-battle Klingon starship.
Don't ask me any overall choices, I would have a hard time choosing. But that's my taste of starships for now.