Organic is ideal, but really any cotton can say it's organic.
Sterile cotton is supposed to not have anything on it (hence: sterile) but I've heard that sterile cotton is often bleached to appear whiter than it is.
My recommendation is finding some Japanese cotton. It comes in really easy-to-use "sheets" rather than balls that you have to unroll, and it also wicks noticeably better than organic cotton. I used organic cotton for about 10 months until this Japanese cotton stuff came around. Also the Japanese cotton doesn't need to be "primed".
With organic cotton (or any cotton I've tried, aside from Japanese) you need to soak the cotton with your
juice and then burn all that
juice off in order to get rid of the weird cotton flavor. After that initial priming though, flavor is fine, no noticeably funkiness.