We store at home, kind of semi-rural, and have a covered area where it lives 24/7. I've heard dryer sheets and used them every year....don't know if it works, but always smells nice when we open up in the spring. In the fall, I take out ALL food and wash the shelves where the food was stored, vacuum the upholstery to be sure all crumbs are gone, wet mop the floor. I leave the linens and kitchen stuff right where it is, but make sure there are no crumbs in those drawers. I always hesitate to say "we never have had a problem" since that will be the kiss of death. I'll just say so far, so good.
Agree that a closed barn-type building would be a great place for critters to congregate, so that would not be my choice. Ours is covered only, but open sides.