I also use the IKEA cardboard magazine holders. I lay them down horizontally and stack them as high as a shelf will allow. They can be clipped together with binder clips for more stability. I can sort paper into: printer, binder, cardstock, small construction, etc. I just have larger construction paper standing alongside because it's too big.
The IKEA brand isn't as sturdy as I'd like--they're kind of flimsy. I've found a few food packaging boxes that are made of very thick cardboard. I like a more "finished" look, so I covered them with old maps, then with packing tape. Contact paper might work as well. This made them sturdier but if I could find a great option to buy, I might not waste the time again.