I have a couple of those plastic drawer systems in my garage where I keep all of my towels, bonnets, and the majority of my pads (pads are also kept and stored in ziploc bags).
As for a towel that I drop on the ground, it's immediately placed into my 'dirty bin'. Further, I segregate towels based on terry, microfiber, and good/average microfiber.
All of my DF Towels get washed separately and air dried. Like ddellwo, I'll wash mine a couple of times before they get to touch paint.
You know what they say... an ounce of prevention...