Choosing a Ship
There are tons of ships in STO which can make it a bit overwhelming when deciding what kind of ship to use. To start let's break down all of the ships into three simple categories:
Tanks - These are usually large ships that move and turn slowly but can take a lot of hits. They are the best for distracting enemies while your Damage ships cause damage. Some examples are cruisers, carriers, heavy warbirds, and battle cruisers just to name a few. They can also be used to cause lots of damage and support your team by healing them or debuffing the enemy.
Damage - These ships are generally smaller, more maneuverable, and can equip cannons. Due to this they can turn to point at an enemy quickly and fire all of their cannons to cause massive amounts of damage. Since they are quick they could also be built to distract enemies. High speeds and healing abilities could allow them to survive a long time. Some examples are escorts and bird-of-prey.
Support - They can be mid-sized ships with a nice balance between Tanks and Damage ships. The primary purpose of these is to support allies by healing/buffing them, debuffing the enemy, and of course causing damage. Some examples are support vessels and science ships.
The best way to determine a ship's role is by looking at its size, bridge officer stations, console slots, and your captain's career. For example, a Tactical captain can boost damage so you should expect the ship you are using to be able to cause more damage. A ship with high ranked science bridge officer stations would fit the role of Support better than Damage.
When doing PvE (which is when you battle the computer) you don't need to worry as much about which ship to use. I'm not saying that you shouldn't try to be good, but it's different than in PvP (player versus player) because it requires more planning and strategy.
The important thing to remember is that there is no quick fix and that no particular ship is better than another. It's a matter of figuring out the ship's strengths and weaknesses then working towards improving it. You can't expect to be the best over night, but with some work and understanding you'll get better.
Now that you have a decent idea of what to look for in a ship you can decide what direction to go in. Fly safe!