Gayla, it is surprising that people don't know about a button jar or box, but when you think about it, these days clothes are usually donated to organizations or passed down intact to friends, neighbors, relatives. In older times, people would wear clothing until it could no longer be worn, then buttons, snaps, other fasteners would be removed. The cloth would then be made into rags if of no use as clothing, or cut into strips for rugs, or pieces for quilts. If people are into the donation of clothes, the most they would have as extra buttons would be the extras that come with garments when new. I think even pockets might be saved for use on newer garments as a shortcut.
Last night I found two whole new categories among the bags of buttons: cufflinks and belt buckles. My old canning jars and canisters are holding more than foods these days!
I have one of those jewelry organizers that will hang up -- one side fabric and the other plastic pockets. I keep cards of fashion doll buttons in this, as well as tiny trims suitable for fashion doll wardrobe items. I think the fashion doll buttons are 1/8", a trifle smaller than baby buttons. Were you the one going to create a box for baby buttons?