I would leave larger pieces as a single piece. (Your choice on what constitutes a largerpiece). Get other ideas at
www.quiltville.com.
I leave pieces as they are and store scraps in a ziploc large bag, with some separation in smaller zip-loc bags. The smaller bags get 2x2, 2.5x2.5, 3.5 x 3.5" squares. I also have a plastic bag for bonus half square triangles. 1.5" squares are in a separate bag to give away, since I don't want to deal with them. I suppose I define scraps as anything smaller than a fat quarter. Larger than that are folded and stored with yardage. Strips that are already cut are left lying around, but should probably be stored in a single place. I don't have any more than would fit into a shoe box.