To keep your dishrag nice and clean and sanitary, put it in your dishwasher with your dirty dishes. I do this all the time and always get compliments on my dishrag looking and smelling nice.
My dish cloth is always full of rich suds. Every time I want to wipe the oven door, etc., I have to rinse all those suds from the cloth. A waste of detergent, water and time.
As I have gotten older, I have discovered the best dishrag for me is actually what is known as a barkeeper's towel. It's certainly bigger than a dishrag but more of a square shape than a tea towel, and is made of really absorbent cotton with a great nap to it.