For single sheets, I bought a file cabinet from the craft store. The file folders for it are so cheap! Only about $3 for 50 at Office Depot and they also sell the "rails" to hold the folders on too! (under $5). I "File" my paper under categories like Card stock, Pastel, Parchment, or under colors like Reds, Blues, Greens, or patterns like Flowers, Plaids, Poka-Dots, Animals, etc.
I've also hung a "PEG BOARD" in my crafting room for tools, tape, wire, my heat gun and lots of other things. I can see them, so I can find them easily!
If the ribbon has tiny holes in the spools, then just thread a piece of ribbon or yarn through each spool Then tie these to a shelf or wall. (A thin dowel threaded through the ribbon spools works even better!)
Full pieces of construction paper can be stored in file folders or in those magazine storage boxes. You can also spray paint cereal boxes to put your paper in. I use baskets and candy tins of different sizes. Zipper freezer bags are great and I have just recently discovered the new Folger's coffee cans (all because DH got mad at Kroger's, bless him). They are plastic with a peel off seal so you don't have to worry about can opener cuts. When I empty one I just put it in the dishwasher and store it on a high shelf till I need it.