I want to show you how I store all of my ribbon. This, by no means, is the "best" way to store something as valuable as ribbon/string/trim. It is what works for me right now.
In the bottom of one of the biggest baskets, I have a plastic container that holds all of Oma Miller's vintage ric-rac and trims. I LOVE these vintage trims.
Then I sort all of the ribbons, by color, into ziploc bags. Because I have lot, I have to make sure to smoosh all of the air out of the bags so they will fit in the basket! The large bag on the right contains all of the trims that don't fit in a category. The bag on the bottom, second from the right, holds elastic. I keep any "glittery/sparkly" trim in their own separate bag.
I then put all of the bags into the basket and slide it into the unit. I don't store Christmas ribbon in this. I keep it with the Christmas wrappings.