I have very limited storage space for my stash, so what I do is keep any scrap that is fat quarter size or larger ruler folded or folded on comic boards in my storage units that are for yardage. If it's smaller than a fat quarter, but there are multiple pieces, then I wrap them together around a comic board and they go in a drawer that's for scrap pieces I don't want to cut. Anything that is smaller than a 10" square gets cut into the largest size I can get out of it. I store these precuts in their own storage unit by size and value. So 10" squares are separated into 3 piles, light medium and dark. Same with 5" squares, 3.5" squares and 2" squares. I also store some 2.5" strips if I have a scrap that is longer than 10 inches. By cutting my scraps, I have been able to maximize what little storage space I have and I find that I am more likely to use them that way.
Everyone is different, what works for me might not be a good fit for your way of working.
Rob