I also use welded wire skirts. I just lay the skirts on the ground, around the entire outer perimeter of the coop, attach it to the vertical portion of the fence with hog rings every 4-6 inches, and tack down the skirt with 6" landscape staples. The combination of the vertical fence and the horizontal skirt looks like an "L," with the horizontal portion on the outside of the coop. The landscape staples keep the skirt flat on the ground, and the lawn will grow up through it and with time will pull it into the ground 1/2-1 inch. You can mow over it, and no digging required. Nothing can dig under this design unless they figure out that they have to back up two feet before they start digging.
2X4" welded wire is very strong, and I use it for the sides and top of all my overnight runs. However, a raccoon can reach right through it and easily kill a chicken. Hardware cloth isn't very rigid, so can't be used easily as a sole barrier, but will prevent a raccoon from reaching through or a mink/ferret/rat from walking through. So each wire has its weaknesses, but when used together, one attached flat against the other, it creates a very strong, impenetrable barrier. When attaching the hardware cloth to the welded wire, I use hog rings every 6-8 inches, both horizontally and vertically.
It is essential to avoid gate fasteners that are easy to open. I previously used a minimum of three different types of fasteners on each gate, hoping that if a raccoon figures out one, it probably couldn't figure out all three. Then I switched to padlocks. As one of my friends said, a raccoon may have intelligence, physical strength, and dexterity. but it is unlikely to figure out that the key hanging a few feet away needs to be inserted into the lock to be able to get inside.