So here's where I'm at right now.
Federation:

As I said, I didn't want to get bogged down in Federation ships... there are a TON, especially variations on the Enterprise. Instead, I opted to get two: The Enterprise D (main ship of TNG) and the USS Defiant. They're the flagships of my favorite Star Trek shows, and many of the others start to blend together.
Klingon
I'm meh on this one... it's a pretty basic BoP, but I'm not 100 happy with the deco. The intent was to make it like Martok's ship (smaller, with red paint on the underside, basic BoP) but the decos I saw when I made it seemed to only have both top and bottom. I might try another version.
Romulan
So I waivered a bit on this one. I actually would have preferred the T'liss Refit from Picard, but it's not available because rights. I still opted to switch to a different paint job for it, since as I said I'm not really fond of the green for both Romulans AND Klingons.
Vulcan
Would have preferred this one in more of a magenta-y color, like in some of the show, but it wasn't possible in game so I went with this instead.
Borg
STO doesn't have an option for getting Borg ships, at least as far as I'm aware, so instead I opted to get a 6" Borg cube micro computer case, since that was still far cheaper than the minis of comparable size and quality.
Cardassian
This one was pretty clear cut for me... there are a few others, but the Galor class is the standard Cardassian ship, it's the type of ship Dukat has before his demotion in season 4, it's the ship based on their species logo, etc.
Ferengi
Haven't bought the next two yet, but I feel like the D'kora class is pretty set in stone as my "Ferengi" ship. I wavered because I was sort of trying to match ships to characters, and Quark is the quintessential Ferengi, and this isn't a ship he's ever used in the series. However, the ship I do associate him with, "Quark's bounty" is UGLY. Now, technically in STO there is a variation of the D'kora that's named after Quark, but the only difference seems to be the size... and frankly I don't care about scale differences beyond a vague "big/small" dynamic.
Dominion

This is the one I'm still the most torn on. I'd say the fighters are more iconic, but I'm not THAT fond of the design. In the end, these are the two I'm torn between: The one on the left is a Jem'Hadar battleship, and it's the more beefy ship we see most in DS9. The one on the right is a non-canon ship unique to STO... but it's also Odo's flagship in that game. Part of the reason I'm torn is, the former is a very muted in terms of color (in some ways resembling most of the Federation ships), while the later s sleeker and more starkly colored.