Choosing a Federation Ship
Once you reach the rank of Lieutenant Commander you are awarded commission of a new ship of your choice. There are three main types of ships you can choose from: Science, Escort, and Cruiser. It may be difficult to decide what type of ship to choose so I'll give you a few tips and ideas on how to decide.
First of all, and the easiest solution to this question, is to base your decision on your career. A Science Officer would use a Science class ship. A Tactical Officer would use an Escort class ship. An Engineering Officer would use a Cruiser class ship. This gives you the best combination of skills, however it is not necessary to do it this way. Here is some information about each type of ship in order to make your decision easier.
Cruisers : These are the largest and most resiliant ships, but are slower and don't have the best manuverability. They have a large crew compliment which gives them a fast repair rate. They have more energy than the other two classes allowing them to distribute more power to the subsystems. They adapt well in battle and do well on there own but are also great support ships.
Escorts : These are small and fast which make them hard to hit. They have a small crew compliment which doesn't give them a fast repair rate, however the strong hull protects the crew. Their shields aren't the strongest but they make up for it with the strong hull. Their weapons are also very powerful, and are the only ships that can use cannons.
Science Ships : These are excellent at detecting an enemy ship's weaknesses and cloaked ships. Their weak hulls are protected by extremely strong shields. They can also target an enemy's subsystems. They make great support ships.
Now that you know a little bit about each ship you can decide based on what you like best and what roll you would prefer to play when teamed up with other people. You can also decide by what looks nicer to you, or by what shps you liked in the Star Trek TV shows and movies.
In any case, whenever you pick a type of ship you should stick to it throughout your career. It isn't a good idea to switch ship types everytime you reach a new rank because you won't get the full benefit from your skills. This also lets you learn more about that type of ship which is helpful in the long run. However it is not necessary, you can switch from ship to ship if that is what you really want.