Dont store a shotgun in a zipper enclosed gun case.
Any moisture in the case or gun will attack the gun metal...
Also, to the OP: When buying practice ammo, buy quality shells like AAs that can be reloaded. A buck or two more for a box is worth it. Save your empties and store them in a paper bag in a dry place.
Use eye and ear protection when you shoot, and buy a cheap cleaning kit too, and use it every time your shoot. It's really pretty easy to clean up a pump shotgun.
And above all, don't store it in a case. A case is only for transporting it. Oh, and to answer your question if you're going to be carrying this shotgun on a 4-wheeler I'd suggest a scabbard rather than a case.
I'd use a case to transport the gun from home to wherever you go 4-wheeling, locked up in your tow vehicle.