PIN IT! If you don't have any clasps you can use a safety pin. Use a small piece of felt sewn over the fixed bar of the pin and a crisscross pattern of stitches to sew the safety pin in place - I've used bright felt and thread here to show this clearly:
Laundry Basket in Closet. No need for hampers and can take it straight to the laundry. what a great kids closet! Do 3 baskets, white, colors and darks. Also get different color baskets so kids can sort.