I came at quilting as a way to use up scraps, at first, so I used anything. I still prefer to use what I have on hand. But when I buy new fabric and batting, I buy cotton.
For thread, I use poly-blend threads a lot. Sometimes cotton machine quilting thread. I was recently given a huge box of thread, and most of it isn't cotton, so that will be what i use for the foreseeable future.
For batting, I prefer cotton but have used a lot of polyester (My first quilts were poly, because I didn't even know cotton batting existed. The place I bought batting at didn't carry cotton.) I have a lot of polyester batting that was, again, given to me, so for baby quilts and charity quilts, that's what I'll be using until it's gone.