Lay the collet rack down on its back is a good idea if you have the wall space. Like in a shallow rack in back of or above your working area. And you get to see the diameter of the collet directly. Most machinists are highly tuned to small visual differences in things like hole sizes whether or not they have something close for comparison. If your collet sets live in a drawer or shallow box make it so there are short wood dividers between each rack so that when you take a set out and close the drawer the adjacent set doesn't tip over into the open space and let things get loose.
If you have access to a big table saw and a dado head or similar woodworking capabilities make some channels out of 2x lumber scraps and set them up to hold your collet sets. Once you are set up to do this there are lots of other tool holding and storage blocks you can build on a cool autumn afternoon... expecially if you have some of those nice specialized wood drills that cut the hole edges without tearing out chunks between the grains. Sure beats raking leaves.