Flats and Folding Boxes
One way to store specimens is in foldup boxes in flats. Flats are jus the boxes you used to get beer and soda in. They are approximately 10.5 x 15.5 x 1.5 inches. While 1.5 inch deep is the standard for beer and soda flats, you can get deeper ones from one of the suppliers below.
Denver Box LLC - I've ordered from them and a friend uses them. We have had good experiences.
Tucson Store Fixtures - I have not used them but they seem to have a very good selection and prices.