In the launcher you will see you are likely on holodeck as to start it will say Star Trek Online - holodeck
The other options if you have signed up for them are:
Star Trek Online - Redshirt
Stra trek online - Tribble
Red shirt is where things are tested before they go to holo deck and Tribble is where they are currently testing free to play. By default if you havent done anything you will be on Holodeck, so just earn a bit of cash and you can buy another ship. If you dont have the room just discharge the ship you used at lieutenant Commander to free up a ship slot.