A good tight weave bag like wils makes is better than paint bags. but paint bags work. I wouldn't use multiple bags. you do want easy access to the inside for the occasional stir. You could go buy a $9 polyester shower curtain and cut a square out of it, that'll fit your pot loosely. Use a bungy cord or something to secure it around the outside lip of the pot.
Cleaning? here's how i do it. Dump the grain, turn it inside out, rinse and let it dry dirty hanging from something. Once your done brewing, it'll be dry enough that the stubborn grain bits will fall right off with little effort rubbing the bag against itself with two hands. Then wash it in a bowl or pot with water and a couple drops of dish detergent and rinse thoroughly.