I'm not recommending anything but will share what I do.
I'm a tosser. I'm more profitable if my mind is free to explore the framing world. I get claustrophobic, scatterbrained, and short tempered when my workspace is a mess.
Once I get a pile of matboards I donate everything smaller than 1/2 a board.
For FC bigger pieces go into the bin with full sheets. For those 10" - 15" strips I have a box beside the wall cuter. It's not a large box but it will hold 30 or so strips of FC. When that's full I start replacing bigger strips with the smaller ones. The smaller ones end up in the trash. But I never keep more strips than that box will hold.
I'm heavy handed with glass. Anything smaller than 10" or so, regardless of length, gets busted up. As I pull first from the cut pile, I find that pile doesn't grow much. It's sometimes bigger and sometimes smaller but all in all it stays a manageable size.
Fabric? I don't make dresses. If I did, I'd still toss anything that wasn't likely to sell. The bigger pieces I'd probably fold and put in small shoebox sized Rubbermaid totes (man I love those things). I'd stack those nice and neat with a small piece of what's inside taped to the outside.
All in all I prefer a cleaner more productive work area rather than hanging on to every dime I can in stuff that may or may not sell before it's destroyed in a pile.