I decided to take some photos. My "system" has layers.
The upturned lid of the large shoe box is the top layer. It holds ziplocks of twisted cord, upholstery braid and rat tail, plus a couple of spools of gift wrap ribbon.
When I remove the lid I expose the next layer which contains ziplocks of loose ribbon, silk ribbon, fold over elastic and ultrasuede scraps.
The bottom layer has the spools of ribbon. The larger spools are just tightly packed but the smaller spools are skewered by a dowel and held by elastics.
I also have some trim stored in a sewing basket. The bottom layer has bias tape, piping, blanket binding and rick rack. (Most of this came from Jill, went to my sister and came back to me.) There is some lace and wide eyelet wound on cardboard against the back wall. The layer above has a ziplock that contains some narrower lace and a spool of strung beads.