I use old t-shirts to clean chains. If you cut them up you get 2-3 good rags out of each. For cleaning the bikes, I have an old sponge that probably needs to be replaced now that I think about it. I also will sometimes cut up an old garage towel and use that as a wash rag or to clean the chain.
Once something gets used on a chain or just otherwise gets loaded up with grease, I don’t wash it. I just throw anything past its usefulness in the trash.