Every stamper has to face the dilemma of how to store the stamps. The solution for each stamper varies by the number of stamps (and how often you acquire more!), the space available, how the stamps are mounted, and how much money you want to spend.
I’ve got a lot of stamps. I’ve never counted them. (A hoarder’s denial maybe?) Probably about half of them are mounted and half are unmounted. (Most of the “unmounted” are more accurately described as mounted on cling ushion for use with acrylic blocks.) My craft area is about a quarter of a large room, so I have a reasonable amount of space available. I tend to lean toward makeshift and second hand stamp storage rather than spending a lot of money on new storage units. This is how I store my stamps.