I sort mine into color groups (reds, greens, etc) and then store them upright in a slotted storage cube from Hobby Lobby. It works pretty well for me because I can easily see the colors and choose what I need without having to move a lot of stuff.
I have a ScrapRack. I store by theme first (so like Animals, Birthday, Family, etc), then Calendar (spring, summer, autumn and winter) then color (ROYGBIV). The ROYGBIV goes into Paper Handlers below the Scraprack on a Ikea unit that is a 4 X 1 cube turned on it it's side on wheels and it holds 12 X 12 paper easily.