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I have a set of metal alloy wire shelves (Elfa from Container Store) on my garage wall, with plastic old-style, but contemporary, 5-sided square milk carriers that each have folded and dried microfiber towels, detailing products, etc. inside them. Those containers can be pulled off the shelf if need be or placed on their side for easy access to folded towels which I can quickly grab when needed. I purchased some cheap gray bath towels at a home store, and then some cheap clamps at Home Depot, and have those bath towels clamped on the top shelf, hanging over the shelves containing my detailing supplies. This solution provides air flow in case I don't have something completely dry, but keeps dust away from all my detailing stuff, and the gray towels are easy to lift up and temporarily store on the top shelf when I start work and want to access my stuff on detailing day. It looks clean and tidy in my garage most of the time, and every few years (yesterday as a matter of fact), I just unclamp the gray towels, throw them in the washer and dryer, and hang them up again. It's proven to be an excellent solution for me.
Plastic storage containers with lids you can find at Walmart are great for most things. If they don't fit or are more used, I have 5 gallon buckets with lids on them since my work throws them away usually
1 plastic container for wash mitts
1 plastic container for general purpose MF
1 plastic container for interior MF
1 plastic container for extra plush MF
1 plastic container for WW MF
.... you get the idea