Looks like alot of quilting/sewing areas I have seen!!!!
But seriously, seeing unused plastic bins ... I would probably use the large ones for backing fabrics. VERY large cuts. Also a large bin for uncut pieces less than 3 yards. STASH THE BINS ON THE FLOOR!
Then use a same size bin/s for scraps. I never ever sort scraps. The reason being when they are mixed, you see fabrics going together so well that you might never have thought of putting with each other.
Larger bins come in handy for fusibles, freezer paper rolls etc. Again store any LARGE bins on the floor..clear a spot and stack them.
The next would be to conquer and divide fat quarters. Divide into perhaps dark, mediums and lights. NOT COLOR that gets confusing. Next around, those fabrics you have cut into but are still a good size piece - These I would fold and stack on shelves - no bins there.
From that point, you should be able to see your own space working better for you. This is allow you to see better storage for many items. I store threads in see thru "sweater" size boxes, each box a different spool size. The have to haves that a hard to shelf and store. Also do not forget extra cutting things like scissors etc. I have a group of them handy to use in a clear plastic shoe box. Use the shelves you show us in the pix for this.
Also, howabout some shallow shelves in the wall near where you iron? Spray startch, etc. And have a few pins catchers or cushions scattered around the room. WOW does that make life easier.
Best advice I have received is to not store anything in a container you can not see through. Out of sight, out of mind!
Take it slow, and think it out. You willsolve this!!!! YOU QUILT..if you can organize pieces of fabric cuts into a quilt, you can do this!
Julie