I'm hoping to score some old chainlink fencing on cl or freecycle to build our run with. But I am considering putting hardware cloth around the bottom perimeter as well. We also have coons and possums here. Our dogs are good at keeping them away but with my luck on a cold day they'll be in the dog house and miss something.
We use a 6x8 dog run for our inner run. I had left over 2x2 5' fencing that I used for the top and bottom. Afterwards I lined the sides and top with chicken wire, we attached it with lockwire. SO you get the strength of the run and the small hole size of the chicken wire. The fencing on the bottom we covered with dirt to protect their feet. It's fort knox protected.
That's what I have for my girls. I don't worry about coons because the feather people are locked in their coop at night. It's just as well, because I don't have a top on it. It is six feet tall and so far only one chicken has flown up to the top, perched and looked around and then flew back down. This is at 5 months. I'm hoping that when they're older and heavier this won't happen anymore.
Take a look at my BYC page, we used an old dog run we had and set up our run the end of Februay, so far so good...we did use zip ties to attach chicken wire all along the bottom, around the full run, it helps with the spaces between the panels and the gate too. Then for added insurance we took old fencing we had, bent it in a L shape, zip tied the top to the chainlink and used landscape pins to hold it down so the grass could grow through it. Just in case something decided to try to dig in.