I made a set that are 13" square, and finished them with a rolled hem on my serger. The fabric is 2 layers of 100% cotton, and they seem to wear pretty well.
You could also cut your squares and sew them right sides together. Then turn them and top-stitch.
Makes me wonder what those heavier restaurant napkins are made out of. Those just have a narrow hem all the way around.
Good for you, for going green!