I only painted the outside of the coop, not the inside, and made sure it had time to dry completely before the chickens were locked in it for the night in case the fumes were bad. I just asked the guy at the hardware store for a good outdoor paint for a wood surface (my coop is wood) and went on his recommendation. I don't find that my chickens peck at the coop and are scraping/eating paint chips (I have had parrots indoors that do this, so yeah, it can be a concern with some birds). Lots of people paint the inside too, I'm sure they could recommend a good paint for that.
I just have a piece of plywood on the windiest side of the run that blocks some of the wind and the chickens have figured out to huddle behind it when it's gusty. It also creates a shady spot during certain times of the day.