I unmounted all (or, in the case of my old SU sets, never mounted) my stamps and use...
Univenture binders: 3-ring Closed Binders in multiple colors
case of 15 for $62.25, or call and get better pricing for a larger order. Be sure to use a coupon code, which you can get from their newsletter & FB page. I buy in bulk with a coupon and it's very reasonable.
These are the large size that hold 8.5x11 panels/paper/chipboard.
These are perfect for storing clingmount & clear stamps on the storage panels, and for storing wafer-thin dies on magnetic sheets. They snap shut securely (closed on all sides, so nothing slips out) and sit upright without tipping.
For those considering the binders, sign up for the Univenture newsletter and like them on FB, and then wait for a coupon code. Their site for small orders is UniKeep.
EZMount Stamp N' Store Storage Panels:
These fit in the large binders (above) and are smooth so the stamps cling to them.
These used to be hard to find, but as more people have gone UM, more places sell them. Try Ellen Hutson, Sunday International, Gina K, eBay, or Google.
In each Univenture binder binder, I can fit 3 panels with rubber stamps on thick EZMount on both sides of the panels. I have 4 panels in a couple binders because I wanted to keep those panels together, but they are tight. If you use clear stamps or stamps with the thin EZM or stamps that have no clingmount at all, you might fit 5 panels.
To guesstimate how many stamps will fit on a panel, lay your stamps on a sheet of 8.5" x 11" paper.
For die storage, I can fit 8-9 sheets of chipboard (not a storage panel) covered with magnetic sheets (or strips of magnetic tape) full of wafer-thin dies.
Get anywhere. It used to be a bit hard to find, but many sites sell it now. Be sure to calculate shipping. Sometimes that really skews the overall price. I prefer EZMount to other products I've tried (Alene's TIO&O, thin cling plastic, thin clingmount, etc.).
Of course, after I started this system, SU came out with clingmount stamps in the nice, clear DVD cases. Still, I prefer using the binders because I can fit so many more stamps in them, and sort them by subject. (Yes, I break up sets, but since I don't use the labels, I keep those sheets filed so I know which stamps go in a set together. Not that I've ever sold off a set!)