I, too, make t-shirts quilts for customers. I use Pellon 906F fusible backing, it's a nice weight, not too stiff. I have used many types and found this the best.
For backing a quilt, I always use cotton quilting fabric. Using the best fabric, to me, is the result of a quality product.
For batting I use a medium loft poly by Mountain Mist, it has a nice soft loft to it. I have used others but this seems to do the trick. T-shirt quilts can be quite heavy and the poly batting is very light. Just my preference.