My advice is to not wash the top, as you risk turning it into a wonky mess. The safest way to wash a top is to first baste it (thoroughly) to a muslin foundation. However, I really think this is unnecessary in your case. Most fabrics these days don't shrink enough to make a difference.
For the backing, I would simply recommend using heavy starch on it before layering. I like a 1:1 solution of Sta-Flo and water, "painted" on with a large wall painting brush until fabric is saturated, toss in dryer, then iron with steam. This stabilizes the backing so you are unlikely to get puckers or distortions while machine quilting. I would also spray starch the top a few times to add stability.