The usual recommendation is to use 1/2 inch or 1/4 inch hardware cloth. It depends on the predators you are trying to keep out. We have lots of weasels in my neck of the woods (along with raccoons, bobcats, skunks, mink, fishers, skunks, coyotes, bears, cougars, hawks, eagles, falcons, dogs, cats and probably a few others I have not seen yet). I have read here that a weasel can get through an opening the size of a quarter. They are nasty little things, and can devastate a chicken coop in a single night.