Light, Non iron, Quick Drying, No pockets (never use them on a shirt), UV blocking with a decent collar, short sleeve (I only end up rolling them up anyway). Nice length to them to wear untucked. Vented underarm. Covered buttons to prevent snags. Hanging point for drying.
Hate to be that guy, but non-iron cotton shirts contain a lot of nasty chemicals. You can increase creasing resistance by adding synthetic fibre. Which incidentally also reduces drying time, and wear resistance.
I'm with you on the covered buttons, or more correctly hidden buttoning. Or fly front. Covered buttons usually denotes buttons covered with cloth, fabric or leather. I think this is vital for pockets as well (if you want them that is).
I can't understand what's with the RTW industry as mens wear starting to get shorter and shorter, today you see skinny pants with the cuff above the ankle, lounge coats ending almost over the bum, and coat pockets above the waistline, shirts which are impossible to tuck in because the ride up all the time, ugly and impractical. A decent shirt should go at least to the groin in front and right beneath the bum in the back. It makes it easier to wear both untucked and tucked.
To increase the shirts life I would like to have epaulettes (reduces wear from backpack straps) or a reinforcing fabric over the yoke (which should extend over the forepart, also lessens the problem with chaffing from the shoulder seam). I would also like bar tacks at the usual stress points (something which is usually lacking in the lower end of the price spectrum).