I store my king (big) spools in those three plastic drawers on wheels units for closets. The drawers make for quick access and return after use.They are roughly in color order (by the rainbow) and each drawer is labeled. They are stacked two high to the left and right of my machine. Smaller spools, I found a shallow drawered plastic unit. Serging and regular sewing threads are stored way away from these so there is no confusion.
Great idea! I think I'd like the drawer idea better than storage boxes I have. You have to open the top to get to the thread, so I have to unstack first. I'll have to check them out.