I use a similar storage cabinet, a 3-drawer unit on casters, from Sterlite:
I still had the issue of being able to tell what color some bottles or jars of paint are.
As was mentioned above, I do mark my Testor enamels with a dot of the color. But I only have about 20 bottles, in a small range of colors. That includes "active" bottles, currently in use, and their backup supplies.
For small round jars, like Tamiya, the old Model Master paints, and Lifecolor, I use small gummed labels or price tags, and I write the designations on those. Whether in a drawer in the Sterlite cabinet or in the bottom of my tool box, I can tell right away what each one is:
For eyedropper bottles, like Andrea or Vallejo paints, or the craft store paints, I need to see the labels. Eyedropper bottles have tops that are too small for drops of paint to help, especially with colors in a range, like flesh colors, shades red or brown, etc. And the craft store paints have colored labels on top of their caps, but again, some are so close to one another, that I really need to read the lablels.
So I made a little rack out of scrap luan plywood, to hold the bottles at about a 45-degree angle. That way, I could read the label when reaching for the paints. Here's a photo:
By happy accident, when I got a large toolbox to take my gear to club meetings or modeling meetups, the rack fit in the bottom of the toolbox: