The biggest thing to do when you store a RTT is make sure it is put away dry - it also wouldn't hurt for it to be clean. I don't worry if mine are stored on their side or flat. What I don't do is put significant weight on them.
I also store my RTTs off the ground and usually on top of a few boards. This keeps them off direct contact with the ground to keep down on abrasion and water damage if an area floods.