For what you are doing nails are fine. I know there are people that like to use screws, but it's really not needed for an in place coop. We do use screws for any kind of portable structure we build around here because nail construction pulls apart much faster when stressed that way, but I don't think you need to go to the extra time or expense for your coop. Happy building, it sure feels good when it's done and the chooks move in!