The Nova class gets my vote, hands down. A little biased, as I used to sim on one in a different Trek game but there's something intimate about a small survey ship. I feel like you can get a really compelling story going since the crew compliment is so small. I mean, you could put a name and face to every member of the crew quite easily! And that adds to the peril of something happening to any of them!
Defiant is choice number two because that thing hits way above its size, and the nose art potential (as mentioned earlier) is just fantastic. Also, it had the best concept patch ever.