Feds, Klingon and Romulan each have different flavors of ships. While cruisers, science vessels and escorts are the main ship types, there are also carriers, raptors (kdf), battlecruisers (kdf) and bird-of-preys (rom).. all of them play a little differently.
You get to upgrade to a new ship for free at levels 10, 20, 30 and 40 (and 50 if you are a paid subscriber/lts player). So I suggest playing different types of ships at 10, 20 and 30. See what kind of ship you're more comfortable with playing so you can make an informed decision when you pick your final free ship at 40 (or 50) since you are likely to be stuck with that ship for a while.
Once you get to level 50, that is the time you may want to buy better ships. but we'll leave the advice till you're close to level 50.