An inexpensive way to store your zippers makes use of aluminum shower curtain clips. Cost is about 99 cents per bag of metal shower curtain rings from Walmart,  or your local Bed Bath and Beyond store or the Dollar store.

This keeps them sorted by size or colors and straight, ready to use.

Clip them in plastic chain from Lowes a few links between each clip.

This works for zippers with the hole in the zipper pull, not invisible zippers. For invisible zippers you can use drapery pins through the cloth end on the zipper.