I use a very thin pillow when sleeping on my back. I find sleeping without pillow a bit uncomfortable. Although I am sure I could get used to my head being pushed back a bit, I still dislike the head just resting on the hard mattress and trying to naturally roll left/right. The pillow helps me keep my head looking straight ahead (almost vertically).
As to mattress, I prefer a mid-to-hard latex mattress with a cover.