Our absolute favorite sheets are our Bamboo Sheets. For a king sized bed, they were about $165 but more than worth it. They are so soft and feel cool. We bought them from Cariloha on one of our cruises (they delivered them to our home at no additional cost). To us, they are worth it. We've had them for a couple of years now (1 set) and they are holding up great.
Why are you worried about wrinkling? Pretty much all sheets wrinkle when slept on. My bamboo ones come out of the dryer wrinkle free and don't wrinkle much when slept on either.