This is what works for me but there isn't a right or wrong way, just different. Almost all my stamps are stored in cheap plastic CD wallets like this:
The CD wallets are stored in cheap IKEA DVD boxes. When I eventually get a craft room (sometime in the next century, probably!) I'll buy some prettier ones! The boxes are marked A, B, C etc then the stamp wallets are numbered A1, A2, A3 etc like the one above.
Cue another boring picture - this is what the inside of one of the boxes looks like:
Each stamp was stamped onto sheets of A4 paper which are then stored in cheap (do you see a pattern here?) plastic wallets in a ring binder. This is what a couple of the sheets look like:
You can see that I've noted the wallet it's stored in, the stamp manufacturer & product code if I know them. The sheets are filed in categories - the top one is filed in Floral Borders, the bottom one in Greetings.
Wooden stamps were unmounted to save on storage space. The only stamps I haven't done this with are large background stamps, alphabet & number sets as that was just a step too far! Organising this lot was undoubtedly one of the most boring craft jobs ever but it means that I waste a lot less time looking for what I want.
An unexpected bonus is that it makes me see my stamp collection in a different way. It's hard to explain, but although a set of stamps will be stored together in one or two CD wallets, I might split them into different categories. For example, a set might contain floral border, foliage & bird stamps - each would therefore be categorised separately so when I come to use them I might end up choosing the floral border from one set & the birds from a different one.
If you're still awake at this point I hope you've found it useful!