I always hang my unfinished tops on hangers that have clips. After folding the quilt, I clip the outside edges of the quilt to the hanger, never on the folds. If you need additional support for the quilt, you can add a binder clip or two over the cross bar also. This way I never get wrinkles or creases in my tops.
When I finish a quilt top I always do the backing and binding at the same time. The back is hung on the same hanger and in the same manner as the top. The binding is put in a zip lock bag. I then punch a hole in the top, above the zipper part, and then hung on the 'hook part. of the hanger.
Doing the backing and binding at the same time I make the quilt top is something I learned in a class with Carol Doak many years ago and has served me well. When the long-arm quilter calls and says she is ready for thequilts they are all set to go and when I get them back I can sew the binding on immediately.