I agree with "Do Not Wash The Top" before it is quilted - unless it is so musty or for some reason you are unable to handle it. It makes a mess of tangles and it is a challenge to press it again after it has been washed. Even when hand washed, rinsed, and hung on a drying rack. (Ask me how I know.)
I would soak the backing fabric in hot water for a couple of hours, wash and dry it on "gentle".
I would do the same with the batting - if it is washable. Read the packaging to see if it is or not.
The reason i would shrink the backing and batting is because - if the top is made from pieces from worn garments - all the shrink has been removed from them.
I have always had some "pucker" in the quilts I've made just from the quilting process.
You might consider using a fairly high-loft polyester batting and tie-ing it if it extremely wonky. But if the fabrics are already fragile, that is not one of the greatest ideas, either.
How much sentimental value do these tops have for you?
I've gotten old(er) and I am having a hard enough "salvaging" my own early attempts made from new fabric.