Discuss with your longarmer what your intended use of the quilt will be... a wallhanging, a much loved and abused child's quilt, a show quilt... she or he will be able to advise you as to the best type of batting to use for that particular need.
I personally don't much care for 100% cotton batting. It's heavy, and it doesn't show off the quilting much. I like 80/20 or 70/30 blends (Hobbs and Quilters Dream) but wool batting is my favorite. It breathes well, drapes beautifully, highlights the quilting, and these days can be washed and dried.
I carry a good variety of batting, but do require my customers to use one of my batts. They're all top quality, and I know that I won't have issues with them during the quilting process. Some longarmers will use what you bring them, some won't. Just ask :)