I store all of mine in plastic display cases. If I have time I will lay down some grass paper as a floor and set them on it, or I will make a simple diorama type base for them.
Being in the military I move quite a bit. This last move the packers wrapped all my models in paper (it was horrifying) and then stuffed them inside the plastic cases wrapped in paper. When I unwrapped them, I was amazed to see that minimal pieces had been broken off, and nothing that wasn't able to be fixed in less than 5 minutes with some glue. I guess these guys know what they're doing.