Don't waste the time and money on chicken wire, you'll get your heart broken when a coon walks right thru it.
Don't bother digging, attach one side of the skirt to the run base and let it lay on the ground (about 18") it will disappear into the grass, you can mow over it, and you can move the run if needed. Be sure to top the run with wire as well as being sure the lower 12" of the run(about chicken height) is a tight weave fence to prevent a coon from reaching thru and pulling a chicken out, piece by piece.
If you have a big enough run, think about setting the coop inside the run or against one side for egg and cleanout access. This reduces the worry of wiring the coop and the birds can go out when ever they want or even, if you give them a outside roost bar, roost outside on hot nights