My game is set in the period after Star Trek VI. I used a refitted Saladin Class Destroyer. My game emphasizes the uncertainty following the collapse of the Cold War with the Klingons and the change in balance of power in this part of the Galaxy. It is a time when the old "truths" have ended and new ones are being created on the "ground". For this I wanted a smaller ship, but one big enough to perform multiple roles in a pinch. The ship is in a border area, so a destroyer makes sense. I wanted a powerful ship, but one that could not dominate in most combats without luck and a good crew. I want the characters to have to be resourceful with limited resources. This also give the crew to move up to a larger ship eventually.
In my new campaign I plan to have the characters get used to the Nova with limited resources and can get to know the crew. After the first season or so I think they will get the Sovereign.