I fold all small leftover pieces inside the larger piece of same
fabric to keep for another project.
To store my fabric, I have purchased tall storage cabinets (at auctions & garage sales) with shelves & doors. Fabric is folded and stored on the shelves sorted by color. (Christmas fabric goes together, 30's fabrics together etc.) Cabinet doors open to have a good view of what is inside. These cabinets don't take up a lot of room, are inexpensive & no lifting of totes!
Each unfinished projects go into its own container.