For storage, I also file my paper in hanging files, but I don't have room for a cabinet so I use three of these. I'm able to slide them under my worktables:
Neat Life Mesh Rolling File Cart with Drawers, Silver
The drawers come in very handy. I was using inexpensive black plastic file crates on the floor and that was working fine for a long while but I just got sick of having to get down on my hands and knees to get paper!
After reading Blueheron's post I realized that, in reality, if I cut a sheet in half for a regular card, I sometimes score and fold the other half so I have some card bases sitting around. But usually I file it in a special file I have of "ready to score and fold" paper. I won't put it in a scrap folder if it's a full half sheet. I guess I ought to file it in its proper color hanging file, but I'm usually just too lazy. Sometimes I remember to look through the half sheets before I cut into another, sometimes I don't. And sometimes I bemoan the fact that I have none of a color left and then "find" a half sheet of it in the half sheet file and celebrate my good luck.