I store buttons like I store small items for my scrapbooking. I get clear fising tackle storage cases from Wal-Mart. They are clear, have a lid, and measure about 2.5 inches tall and 6-7 inches long. The compartments on the inside are able to be changed for smaller or larger items because the dividers are moveable. They stack easily on shelves, and my cats don't like to play with the boxes like they enjoy playing with bottles and jars. I've lost many bottles thanks to my cats.
My boxes look a lot like this:
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