Some battings are much more difficult to hand quilt than others. Wool and polyester are among the easiest to hand needle. Many cotton battings are harder to hand needle. If you really want cotton, I would look for one that is easier to hand needle, such as Quilter's Dream Request; however, you will get very little loft from that batting. Wool is really the nicest.
I would definitely repair any frayed or loose pieces before quilting, and also use harvested blocks to replace damaged blocks. All of this will add length-of-life to the quilt.