I use a poly batting for hand quilting, and a cotton (or cotton with a little poly to limit shrinking) when machine quilting. Because I don't like the batting to shrink the first time I wash the quilt, I prewash the batting if it is 100% cotton. (If you decide to pre-wash DO NOT just run the batting through a wash cycle, just get it wet, spin out the water and put in dryer. Just don't agitate or the batting will come apart. Haven't figured out how to do it with the front loading washing machines yet.)
Different battings give a different look to quilts. Get a small sample, quilt it with whatever technique you want, and wash the test piece. You'll find the look that is what you are looking for.
amh