My family is messy. Often, they are very messy. We seem to have more than our share of spills, mud and unpredictable catastrophes. If we used paper towels on all these things, I'd need to own stock in Kimberly-Clark. Thankfully, we've stumbled across a better plan that works well for our family.
Way back in college, I had white bathroom towels. Over the years, they've gotten pretty worn and were relegated to the "not quite a rag" pile. We started grabbing these full sized towels whenever there was a full size mess to be cleaned, and gradually they've become the go-to solution for whatever needs to be cleaned. Leaking ceiling? Grab the towels. Overflowing toilet? Grab the towels. I don't care when they touch something gross because that is their purpose. Throw them in the washer with some bleach or Cascade and they come clean.
We have used them so much that many have fallen apart. Just before our last move, I went to the local supercheap store of randomness (in our case Ollie's, but similar to Big Lots, etc.) and purchased 10 new towels at $2.oo each. I picked an odd color so that we wouldn't mistake them for regular towels. We've already used them a ton - whenever someone needs to wipe something, they reach for the junk towels.
We're trying to extend this process to smaller jobs, too, without as much success. We have a stack of microfiber clothes that I got at the dollar tree and I encourage everyone in our house to grab those instead of paper towels.
This does add a little bit to our laundry, maybe an extra load a week, but the savings of paper towels is great, and (usually) no one tries to use our good towels to clean up messes.