When I moved I finally reorganized my sewing fabric as follows:
1. The garment sewing phase of my life is pretty much a closed chapter. I donated the fabrics not suitable to quilting to a local refugee group and Goodwill.
2. I purchased stacking plastic drawers next.
3. I squared off the ends of my fabric pieces and cut up those scraps in 2" pieces and larger, whatever seemed to make the best use out of the scraps and put those in mini stacking drawers by size for future scrappy quilts. That took the most time, so I worked on it a little at a time. It works very well to fold the remaining fabric you are storing around a cutting ruler. Slip it off, fold it in half for a neat look.
4. I put all my backing sized pieces in a trunk I own.
5. I have a drawer dedicated to future projects or orphan squares. It also works well to separate projects in cardboard containers with short sides (like soda cans are sold in).
6. I separated all my plain or almost plain fabrics and stored them together.
7. I have a lot of batiks which I stored together.
8. I separated plaids, checks and large prints.
9. I stored the remaining prints by color families.
10. I have a scrap bin on my cutting table and when it is full I force myself to cut it up into usable pieces.
This has worked well for me. I hope it helps you too.