I used cotton duck. I think twill would wrinkle less. When you wash it only let it dry until slightly damp and then put is back on. I found that the wrinkles come out by themselves using this method.

I had chairs slipcovered in a matelasse - I found king bedspreads on sale on line and the price per yard came out to be a real bargain. The fabric is not 100% cotton - don't remember percentages exactly but it's a cotton poly blend and I think that helps it not wrinkle and retain shape very well.