I sort my prints by main colour and stack them on a shelving unit if they are under a yard. I keep all my solids and all my batiks together, again in folded stacks on shelves.
Anything over a yard, I fold and they go on lower shelves.
Backings or larger amounts, I have hanging "boot bags" that are like shoe bags only bigger and hang from a rod in my closet and have 6 spots in which to keep my large pieces of fabric. I got these for cheap at the Goodwill. I also have a couple of the shoe bags and one of them is perfect for keeping all my 2 1/2" strips separated by colour.
Anything that I think is too small too be of use, I cut into strings right away and it goes into a drawer near my sewing machine so I can make string blocks whenever I feel like it.
Any little bits too small for that I'll either toss or keep in one of two plastic boxes to use for collage. One box is cool colours and one box is warm colours.
Watson