Maybe I'm too well trained that everything should be kept in its place, but I store mine in the skinny cupboard with my sheet pans and wire racks. It's round, so it just rolls in and out. The only problem is that I forget about it while letting it cool down after using, so it usually ends up getting put away the next time I use the oven... and then only if I see it before preheating the oven and beginning the entire cycle again.
Maybe I should take Andy's suggestion and just leave it n there.
One comment - if you do use a stone, let the oven preheat longer than usual - much longer than the automatic signal tells you it's ready. I have one recipe that tells me to preheat the stone for 45 minutes before putting the bread in.