Ditto on don't use chicken wire. It is only good for one thing--keeping chickens in. It is NO good for keeping most predators out. A racoon, dog, coyote, etc will just rip right through it and then they have a captive group of prey all cornered up for the taking.
Same as the perimeter fencing. 10/48/3 fixed knot woven wire (class 3 galvanized--cheaper in the long run,) with several strands of high tensile smooth offset from the woven wire. I go taller with my posts and have a couple of hot strands above the woven wire. Hook the high tensile smooth wire to a good electric charger. Don't cheap out on the charger--you want to leave an impression.
To really "Fort Knox" the area add a strand of barbed at ground level attached snug to the fence posts. And/Or add some more woven wire dug into the ground a couple of feet or even just laid flat on the ground and covered with dirt a couple of feet out from the base of your fence. This last is to help prevent digging under by a determined dog/coyote, etc.
This is not the cheapest way at the outset, however, good quality fencing like this should last you 20 - 30 years (depending on where you live.) Getting good sleep at night and not worrying about predators while you are away is worth a little investment.
On the perimeter fencing the offsets are inside (to keep livestock from leaning or rubbing against the fence) and outside (to keep predators away) but for a coop and run they only have to be outside. For most critters one really good zap and they will stay clear of your girls. For a coop and run you should also add netting across the top of the run to keep birds of prey away, especially since they have federal protection and you don't want to get caught shooting the hawks, eagles or whatever you have in your area.
I also mount trail cameras in hidden places in case of two legged predators. If someone other than me is opening their gate I want evidence for the officers and judge to see.
