I've made ours out of cotton knit and flannel, depending on what I had available. They both work nicely, but I think I prefer the flannel. I have used old t-shirts, old flannel shirts, my DH's old flannel boxers, leftover flannel scraps from a baby blanket I made, etc.
The size we like is approx 4x8 inches (give or take an inch in either direction, depending on how the fabric scraps cut), and I make a double-layer. That is about the width of a roll of toilet paper, and a good size to fit easily into an empty wipes container.
I have quite a few that I haven't sewn, too. I didn't have a machine when we first switched over to cloth, so I just cut up old shirts, etc and left the edges raw. It works just as well, but some fabric does tend to ravel in the wash. The sewn ones look a bit nicer and don't ravel.