Are you thinking of hand quilting or machine quilting?
Also, I'm not sure I understand. You need to requilt *before* adding new batting and backing? You mean you are planning to add a batting and backing to the existing quilt? In other words, are you taking off the old batting and backing first? If the existing machine stitching I see is the quilting, I'm not sure how you are going to get all of the old batting out of the quilt unless you take out all the old machine quilting. If this is what you plan to do, I would take photographs of the quilt and then re-quilt by machine following the old plan as much as possible.
For batting, I would suggest either Hobbs wool or Quilter's Dream cotton. Either of these would keep the quilt soft and supple.