You may start out in a heap of junk spaceship to begin with in Plancon: Space Conflict, by HeroCraft, but as you explore the wide open universe you'll have a chance to fly your own battleship. The sci-fi RPG allows you to create your own character and crew, then fight against aliens who have tried to invade Earth.
For some added variety, you can even choose between real time shooting or turn-based fighting when you encounter alien ships. Plancon has a bunch planets to explore as well as lots of ships to buy and upgrade on the black market. Will you choose to be a pirate, a merchant, a thief, or something entirely different?
You can discover the vastness of space exploration in Plancon: Space Conflict for $2.99 on the App Store.