Firstly, old quilts that have had wear and numerous washings are usually fine to use as backings. The problem with sheets is their high, close thread count compared to crafting cottons. If you want to purchase sheets specifically for backs, buy cheaper ones that you can see light thru the weave and prewash them.

Never wash a completed top. As Auntpigly said, you'd end up with a thready mess, and it would be near impossible to press it out neatly without distortion.

I design and sew with precuts everyday. Quality cotton has minimal shrinkage and so I'm not a prewasher anyway (except flannel). If your top is unwashed and your backing is washed, worst that will happen is the back will end up SLIGHTLY wrinkly, not the front. Remember, same thing happens if both front and back are unwashed and shrink at different rates. And for those who prewash, it sometimes happens that one fabric continues to shrink thru another few washes. Yes, I've seen it affect prewashers also. I guess we all have to remember we're working with woven fabric, not wood.

As for thrift shop goodies, go for it. I've used blankets as batting for years and love em!! Don't forget tho it's often heavier and thicker than batting, which will pose its own issues during quilting, especially on a domestic machine with a smaller throat space.

Also, may I mention pressing? If you press with a little steam throughout the construction of your blocks, you've preshrunk your fabric anyway. Not huge amounts of steam, that's the quickest way to set creases and distortions permanently.

Anyway, hope this helps, it's a learning curve for sure!!

Cheers, Pami