Rag quilts are so flexible about whether or not to use batting and fabric types. When I was teaching, my kids would each make a rag quilt. Some would use quilting fabric, some flannel and some fleece. You can put fabric on one side and flannel or fleece on the other. If I were using flannel & fleece, I wouldn't use batting because it would be hot and heavy. We always cut the batting smaller than the square so it wasn't part of the ragged edges but if batting snuck out of the seams, it didn't matter. Batting can be whatever you prefer - warm and natural, fleece, flannel, an old sheet or blanket - use what you want to get the weight you want.
I also recommend snips that spring back open. They are pricey but worth every penny!
Your seams will be nice and full after washing when using cotton fabric.