Recently, born out of a sense of thrift more than anything, I decided to make a major change in our kitchen and cut paper towels out of everyday usage. The most painless way to do this, especially since my husband does a lot of the kitchen clean up, was to replace them with something that resembled paper towels as closely as possible. There are a lot of cute designs for flannel or terry cloth kitchen towels, even some with waterproof backs, or snaps so they can reside on a roll holder, but I knew that anything that looked even vaguely "good" wouldn't get used for real messes. So, I chose to go the very simple route by tearing up a few floursack towels (a dozen for $12 at Sam's Club) into 12 squares each, and taking the opportunity to test out some of the various finishing stitches on my new sewing machine.
I picked up a tip towel basket at Target; it's the perfect size, though truth be told we usually just stuff them in there, rather than folding them as in the picture, so anything that fits on your counter would work (an old CD crate, perhaps?). Our laundry closet is right in our kitchen, so we just have a plastic bin that lives on the dryer for the dirty ones, but a little bag in a cute print could hang on the oven handle to catch the used ones.
We're a small family that does laundry frequently, so 2-3 dozen has us covered for now. We still keep a roll of paper towels under the sink for the greasiest tasks like draining bacon or seasoning cast iron, but it often goes quite some time between uses. The only trick has been remembering not to throw the cloth towels away, as they're so similar to using paper!