I never bought a ship in this game. When I do, will I forfeit my old ship always? Or can I store it so I can switch it depending on the mission?
It is possible to own more than one ship at a time, however it can be a hassle switching between them. When you buy a new ship, your current ship is stored at that station. It will remain there, ready for you to pick it up, but you must return to that station to do so.
For example, say I purchased a Viper from Ngaliba, storing my Hauler there. Then, I fly 120+ LY away and discover an amazingly profitable trade route. My options would be to either fly back to Ngaliba to pick up my Hauler, or just purchase a new Hauler.