transport will be fine with the hull up, just make sure you secure the bow and stern with tie offs to the bumper. Wind turbulence while driving can cause some scary shifting if you don't. And don't leave it on the rack in the sun for long periods because the plastic will soften and dent.
For storage, sounds OK. The best way to store a kayak is on its side if you can secure it that way, but as long as it is well-supported, storing it upside down or cockpit up will both work. A cockpit cover is good insurance to keep creepy crawlies and furry things out of it.
4-place Boat Trailer