We used 1/2" hardward cloth everywhere, including the top of the run and put a skirt around the bottom of the run. The windows and ventilation openings of the coop have hardware cloth . Electric twine fencing surrounds the bottom of the run about 6 inches off of the ground.
We also buillt a large area from the run, in the pasture, so the chickens can go out when I'm at home. This part is not predator proof. I used plastic step in posts, plastic poultry fencing from Lowes, and deer netting on the top to keep out the hawks and the chickens in. When this was first built, we didn't have the deer netting on the top. After five min. one of the chickens flew over the 3' high plastic poultry fencing. Yesterday, we added 20 inch electric poultry fencing because something, I think a rabbit, was chewing holes in the plastic poultry fencing.
I'm hoping this will protect the girls from predators.