Any chance you'd want to edit them down to what you really love or might love? I got rid of a lot because even though cute, I had to face I wasn't much of a sticker/phrase crafter. How I organized the ones remaining happens to fit my current storage units.
1 - Sheets of alphas and phrases are in two drawers in a 3-drawer Ikea unit that fits into an Expedit/Kallax cube but also could sit on a shelf/table. (Enamel dot sheets are there too.) The unit is cardboard but sturdy. Bump-ones or feet that come with it need to be put on the bottom so it won't slide when you pull out a drawer. They may be discontinuing them and solely on line:
http://www.ikea.com/us/en/catalog/products/50272480/
These sheets used to be in pockets, standing vertically but I got rid of enough that I thought I'd try them in the drawers which can be pulled out.
2 - Chipboard shapes are mainly with other embellishments - in SSS 5" pockets standing up in medium Container Store Pure Box. The pockets are the ones Jennifer McGuire recommends for dies. Pure Boxes are inexpensive, light weight and stackable:
https://www.containerstore.com/s/col...uctId=10035361
3 - The tiniest shapes - many stars! - are in a CraftMate organizer; each compartment opens separately:
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
I assumed I was an album person, but found it was easier/faster to have a box with vertical pockets to quickly leaf through instead of turning pages. YMMV.