I keep my stash in plastic - we have 2 cats & 3 dogs so there's always a ton of lint and fur in the air and I want my fabric to stay as fur-free as possible! (of course the instant I lay anything out a cat magically appears on top of it, but that's another issue!)
I use plastic Sterilite drawers for my quilting fabric and I LOVE them. I have a few bigger totes for non-quilting fabrics (like all the fabric I bought to make those curtains I'm probably never going to get to, and some vintage fabric I'm scared to "use up") and then I have a small group of 16-qt totes that are "project" totes; each one holds parts of a specific project and are rotated through as I work on stuff.