I keep my paper in Iris-type containers. I have two carts stacked together that hold 12 containers, then I have others in a pile that will eventually go on shelving. I like the containers with lids so my paper stays clean and neat. I tear my stacks apart, except for a few special themes, and organize by color, but whole stacks can be kept in the containers also, sorted by theme.
I keep my cs & pp together. I think by colors :>)
I don't snap the lids shut since it's too hard on the fingernails to get them open again, but they close enough to keep the paper clean.