I store all my small pieces in those square cardboard decorative boxes that you see at Tuesday Morning and Joanns. I have big ones but I don't see them at Joanns much anymore.
I fold the fabric in to uniform sizes that fit standing up on edge and organize by color. My daughter who is a super organizer started this plan for me and it works. I have to stop now and then and refold when I get too messy. I hung paper tags from them with the colors & info like "Red Green & Blue Small Prints".