Anything you buy at the Imperial Center Store is the personal property of your character and can be used in your stories (character development, squad stories, etc.) For the Squad Stories, however, you may need to check with your SL to see if you would be allowed to use them (if the items are unique).

If you bought a Land Speeder, then in, say a character development story, your character would be able to use that Land Speeder and call it his own. It would be his personal transportation vehicle.