The Sterlite containers that have thin, clear drawers are what I have seen used.
They are also good for the foam alphabet stamps.
You can store them in there, and then take them out, and put a lil soap and water in the drawer, and use that to clean your stamps as you go. Rinse and wipe. When you are done, you dump the water, rinse out the container, and dry. Then, just put your stamps back in.
Pretty user friendly.
hth!
Hugs:)