After you reach Lieutenant Commander you have the option to choose between 3 ship families.
Escorts are small but pack a huge punch, they are very useful in beating the living tar out of those romulans. But what they take in for speed they loose in defence, I wouldn't suggest using escorts against high-level enemy's like the Borg. Escorts have extra tactical slots so you can even add a torpedo spread to your arsenal.
Cruisers are big fat ships that can take a real beating and go along fine. But they have flaws. Due to their large size that cant meneuver very well. They also have poor turning rates. Because they have extra Engineering slots and large crew sizes they last longer in fights like against the Borg. They also can heal faster with certain abilities like those that reinforce the structural intgrety field.
Science vessel can use cool abilities that can mess up your opponent. Tractor beams, science team, rotate shield frequency you name it, science vessels can do it all. In terms of health science vessels aren't the best choice for long range missions.
All three ship types come to equal when put together. Which means none of them are better than the other. But they have some advantages. Personally I choose Cruisers, for one reason is that their big. When you reach captain you can choose from your choice of Exploration Cruisers. Which are Galaxy, Celestial, and Envoy classes. They have certain properties that stand out from the rest of the cruiser classes is that they have loads of shield strength. Keep in mind that Galaxy class has the strongest stock shield generator.
Well there you have it, you know all you need to know about your first ship type now go out there and beat the living tar out of those klingons.
Search for my other tutorial about bridge crew on a planets surface.