Definitely go with 1/2" hardware cloth. We ran ours over all openings on the sides and completely underneath our coop & run to keep out the many determined predators we know are lurking nearby - especially raccoons! (Also covered the top of the secure run as the predators can climb or fly in to get the chickens.)
Raccoons are excellent at opening slide-bolt locks and latches, too, so we secure ours with carabiners. So far, they haven't managed to manipulate those with their too-clever little hands!
I also wanted to keep the pullets from accidentally digging under the run sides - they really love to excavate fairly deep holes!