my sewing space is small, so I have a smallish stash. That said, I store my fabric in those cheap plastic drawer units from Target since they fit under my tables, and keep dust off the fabric. I use comic boards that I cut to fit the drawers. I fold the fabric over the boards, and stand it on end in the drawer with the fold side up. (sort of like filing fabric in a file cabinet that has hanging folders).
I put the cotton quilting fabrics in the drawers sorted by value and yardage. So, I have a drawer that is for anything over 1 yard and all those fabrics are arranged by value. Another drawer holds 1 yard cuts, again arranged by value.., there's a drawer for under a yard, but bigger than a fat quarter also arranged by value, a fat quarter drawer and a drawer for extra wide backings. I have a separate unit where I store anything smaller than a fat quarter. I cut some scraps into sizes that I use regularly-- whatever the biggest size I can get out of the piece-- 10" square, 5" square, 3.5" square, 2" square and 2.5"strips if the piece is long enough.
anything smaller than that goes in the shoebox for string quilting and crumb quilting.
I have a variety of other fabrics that I use in my art quilts and those have their own drawer units--they are stored by type of fabric and within type by value since that works best for me. Some of those are folded on comic boards, but some things like velvets and silk, satins, etc. are just folded and stacked in the drawers. Then I have a drawer for my orphan blocks, bits and pieces etc. that will get used at some point when a project calls for them, and also a drawer for my hand painted and hand dyed fabric--which mostly get used in my art quilts.--Since I dye/paint small pieces at a time and then immediately heat set them, I find that it's easiest to just lay those flat in a drawer that's 14" square.
Looking at the 5 different drawer units I use, maybe my stash isn't that small after all
Rob