Pizza boxes?? You ladies are brave...I would worry about smells getting into the fabric and attracting bugs.
I use 16 qt clear rubbermaid bins for work-in-progress, and also to store fabric together that I'm accumulating for specific quilts. I use post-its to mark what each one contains (although it's pretty easy to tell from what I can see inside, usually). While they're empty they stack together in my closet, but usually most of them are full; I have a table that they stack up on against the wall so I can't "forget" about anything. Raw fabric goes in there; when pieces are cut they go back in there. Unless I'm using a flannel backing, I can usually fit everything for a quilt (except batting) in a single tote. Makes it easy to work on a specific project!