I recently changed tires, from the 20 X 1.5 Marathon Racer to the 20 X 1.75 Marathon Plus. I wanted a very puncture resistant tire, and I like the ride. The Plus is a much heavier tire.
I have 17mm wide rims, and I was able to keep them. I am right on the borderline. If I were buying new rims, I would go with a 21mm wide.