How to create craft paper storage
Buy a sheet (or two, or three - depending on your scale of storage bins) of 1/8" tempered hardboard (Masonite® is one common brand)

Cut 1/8" (or just a hair larger) slots in 3/4" boards (shelves are a good starting point for material in consistent sizes if you don't have some plain wood handy.) 

Cut the hardboard a bit bigger than your paper - enough to allow for both the slots and some room for handling. Glue the top and bottom pieces into the slots. Trying to glue them all might be frustrating ;-)

Cut another sheet of hardboard the size of the back of your two sides plus shelves, and glue and nail it to the back. That will give it a great deal of structural strength as well as keeping paper from sliding out the back.

(Or, visit an office supply store or an office furniture surplus outlet and look at in/out bins, document organizers, mail sorting bins, literature sorters, magazine racks, etc. to see if there's a solution you can just buy. Should be easy for 8.5x11, more of a challenge for 12" square.)