Finding the right storage solution that works for your space can be challenging. Here is my current method for storing cling mounted stamps. I have my wood mounted stamps on shelves next to the desk but I keep the cling mounted ones on my desk. The yellow box (and green one above it) are Rectangle Boxes from WalMart, found in office supply department. The boxes came with two dividers but I needed to use one in the yellow box to support the green one on top of it.
I got the plastic storage cases from Stampin' Up! and they are the same size as a DVD case. (Which means if your collection is larger than mine, you can also look at DVD bookcases or movie racks to store them in.) I cut paper to fit inside the cover sleeve and stamped the images on the front. On the side I've written both the stamp company
I like to keep a personal catalog of all my stamps in a binder, including the digital stamps saved on my computer. This allows me to categorize the entire collection in a way that helps me find the right image when I need it.
As long as it doesn't matter if the stamps aren't facing upright, then it's like a puzzle to see how many can fit together. Once I get it to my liking then that's when I stamp the cover so I can remember the placement. I keep all of my sentiments together so I only have to look in one area. However, I stamp the sentiments a second time with the set they came in so I which ones went where.
I hope I've sparked some storage ideas for your own cling-mounted stamps. Good luck!