Whatever ship you buy for your character is his/hers to keep permanently. Even if you leave the fleet, the ship is still yours.
Fleet gear, especially those of the final fleet tier, is just a handy way for Cryptic to sell players their 'best of the best' gear as it is really expensive to upgrade a fleet holdings. (PS: not all fleet gear are the best, some are actually quite useless. So it may be wise to ask around before you purchase something)