Rule number one; always bring a shotgun. Regardless of how open the terrain and how much you think you will not need it, more times than not it’s those times that you will. Rule number two; leave the shotgun on your lap where it can be thrown to your shoulder at a moments notice should a coyote show up out of nowhere. Rule number three; if you use an electronic caller, always face directly towards it. Coyotes that will commit to shotgun range usually come in on a rope so your shot will likely be in the direction of the caller. Rule number four; do not raise your shotgun until they are well within your comfortable shooting range. If you move too early, when the coyote just gets into your range, there is the possibility that they will see you, do a 180, and be out of your range before the gun hits your shoulder.
Chokes vary depending on preference. As one would think, open chokes are good in tight cover, where quick and close shots are common. In tight cover like this, a full choke would be no more useful than a rifle as their patterns are so tight at close range that you lose the reason you have it in the first place. Full and super full chokes, on the other hand, are great in open country. Here you can take full advantage of their longer range capabilities and although rifles are a must in this terrain, carrying a shotgun as well nearly guarantees you will be taking fur home when they get within 60 yards.