I'm getting ready to do the topstitching on a quilt, with some free motion designs and some patterns with a walking foot. Does rayon thread work well or should I stick with 100% cotton?

I have used cotton, rayon and polyester for quilting :D:D:D

Use whatever you like. Rayon thread has a higher sheen, but may not be colorfast.

free motion quilting you use a quilting/darning foot and lower the feed dogs
a walking foot you keep the feed dogs engaged and do straight lines. you will break needles and have lots of other problems if you try to do free motion designs with your walking foot.

I believe rayon thread will stretch more than cotton, so you would need to adjust your machine's tension.

I've used rayon often in wall hangings. But, I would stick to cotton or poly embroidery thread if you're going to wash it often.

I stick to cotton, but would love to try some rayon. It has such a pretty sheen.

I usually use rayon for stitching around applique and stick to cotton or a poly thread for quilting. Some of the mercerized cotton threads have a nice sheen to them.

I use a lot of mercerized 100% cotton thread, but I love the sheen that rayon thread has! I think rayon is very pretty when you want to highlight your quilting...but rayon can be less than colorfast and may fade over time. They are making high quality poly thread that looks like rayon but holds up much better.
It's your quilt, use what you like!