I've used Promarkers for a couple of years now and store them flat on a DVD rack as in the photograph someone posted ( sorry can't remember who it was)lol
The main thing to remember is to push the caps on until you hear it click. My Daughter was using them and didn't push the cap all the way down and that end dried out slightly. Left the pen stood on it's end overnight and seems fine again now.
I use them for all sorts of things....colouring ribbon, clear gems, peel offs, buttons and paper flowers.