If you don't have a slot available yes you will need to free one up or buy one. Pretty sure that if you have a slot open its available in the ship yard from the ship selection officer;just need to make it ready.If not then it may not let you claim it till you free up a slot and you can always reclaim from the Z-store or the the officer that sells em.
*From ZC-Store is easier then just hit the selection officer.
So, to answer your original question, no, you do NOT get a free ship at 50. After 40, you can buy ships via either dil (the ships from previous ranks that you didn't choose with your free token can be purchased for refined dilithium), ZEN, or through your fleet (the fleet modules will have to be purchased with ZEN but you'll need fleet credit as well).
Also if you mess up your level 40 free ship choice, remember you can also purchase a Mirror Universe ship from the exchange, they are usually priced between 50k and 200k EC.
Available types are the Star Cruiser, Assault Cruiser, Recon Science and Deep Space Science vessels, Qin Raptor and Vorcha Battlecruiser. The fed mirrors are the same as their prime counterparts, only the crew amount differs slightly, and the ship model and skin is changed. Klingon mirrors have entirely different layouts. If you want a mirror escort, you are out of luck, as they do not exist yet, so Fed players should always choose an escort at level 40.