For the white fabric, I suggest going to Wal-Mart or a similar store and buying a couple low threadcount white sheets. The white wrap I used for my Gaara costume was a $4 white sheet from Wally world, and it worked great. (It's also what we used to wrap Kankurou's puppets).
I've seen Akatsuki rings online for about $6, but I'm not sure how much the shipping is. You might be able to find them at places like Suncoast, but I'm not sure.