I've never washed batting and probably never will. I do put cotton batting in the dryer with a small damp towel if it's very wrinkled.
It sounds like you don't want any shrinkage in your quilt. If you use a cotton batting, it will have some shrinkage, and result in some puffiness in the quilt top and backing. If you use a poly batting, it won't shrink, so that's probably your best option.