We did the same, and put some solid polystyrene sheats with plywood backing on the joists for storage. I can't find where we bought them , but I think they were kingspan or similar. They can be cut to fit the joist gaps so that they butt up against each other while their edges are resting on the joists.
Just one thing to remember - make sure all electrical cables are brought above the boards, as the polystyrene will eat the cable sheating, as well as insulate the cables causing a fire risk.