Half inch hardware cloth may not keep small mice out, they can fit through very small holes. A mouse doesn't stand a chance in my coops and runs, they would be eaten in 3 seconds flat, and snakes don't get a chance to grow up! I did not bury any wire, our ground is packed clay, roots, and rocks. I laid a strip of welded wire 18 inches wide all around the outside of my large run, the others have cement blocks as their base. I've seen many dig marks, but no critter has ever gotten in. Mostly I thank God for protecting them every day! How deep you bury the fencing depends on your soil and your predators, and how willing they are to work for a chicken dinner. I've seen recommendations for from 6 inches deep to 18 inches deep. It took me some time to figure out what predators I had because our chickens lived on our property before we built there. I spent most days there, but worried about night predators, so my runs are like chicken Fort Knox!
