Till you reach level 50, there are only 3 type of ships - cruisers, escorts, science vessels.
Science vessels are medium sized, weakest in terms of damage capability but often has special abilities that can turn the tide of a battle. The typical science vessel is Voyager. In general, it takes a player who's intimately familiar with STO's ship design philosophy to get the most out of a science vessel.
Escorts are small, fast, nimble and hits hard but can be fragile. DS9's Defiant is the model escort, lots of pew pew pew, but can quickly get taken down by a volley of Breen torpedoes. They can usually make quick work of smaller ships but may need some skill to take down bigger ships that have bigger hulls and shields.
Cruisers are big and slow but beefy and can take a lot of hits. All the Enterprise ships (NCC-1701 no bloody alphabet, A-F) are all cruisers. They are the easiest to command for new players because they can take a lot of punishment and damage-wise is middle of the road.
My usual suggestion for new players is to try and get a feel for the three basic type of ships so that when you get to level 50, you have a better feel for what type of ship you are more comfortable with. That's when you get access to more types of ships such as Dreadnaughts, Battle Cruisers (2/3 cruiser, 1/3 escort), Destroyers (1/3 cruiser, 2/3 escort) and Carriers (2/3 science vessel with deadly shuttles/fighters).