I keep a number of my rubber stamps in drawers in an Expedit unit from Ikea, and this worked for me for some time until I became a member of the Magenta Design team, and my stamp collection begain to grow quite a lot. I needed another method for storing my Magenta stamps, while keeping my other stamps separate. If you have shelf space available, this storage system could work for you whether or not you need to keep certain stamps separate, and it works well for wood mount, cling or clear stamps.
I got this idea for storing rubber stamps from Jennifer Mcguire, who is an expert in storage of craft supplies. The container I use is called Fridge Binz, and I have found them at the Container Store, Bed Bath and Beyond, and on Amazon HERE. These bins are actually designed for food storage in refrigerator or pantries, but they work very well in the craft studio also.
The bins have a center divider, and each half is over 5.5" wide and over 14" long. I organized my stamps into categories, such as Nature, Flowers, Things That Fly, Christmas, Images, and Sentiments & Current Collection. This allows me to quickly put my hands on the stamps that I need for a project. I stacked the wood stamps carefully in the bins. Take care how you store your stamps so that you don't get a dent in the rubber or mounting cushion.
As a design team member, many of the stamps I receive are cling mount stamps, and they arrive without packaging. I store these stamps in plastic pockets from Avery Elle, called "Avery Elle Stamp and Die Storage Pockets" (You can also use this method to store your dies, by the way). I print out pages of the Magenta catalog that contain the images of my stamps and I glue those to white cardstock cut to fit the pockets.
I place my cling stamps onto acetate sheets and slide them into the pockets behind the cardstock. I can usually fit more than one stamp in a pocket. You can also store your sets of cling and clear stamps this way.
I hope you'll give this stamp storage method a try, or that at least some part of this tip will work for you.