The three most common types of hardware cloth are 1/2, 1/4, & 1/8 inch. It really takes a coon with tinney tiny fingers to poke its mitts through any kind of hardware cloth.
However if you keep your baby chicks in a brooder with a floor of hardware cloth to battle coccidiosis and things like that, be advised that a coon will happily sit under the brooder and nibble off the toes of your baby chicks. A safe coop, pen, run, or walk should start with a good stout strong perimeter fence that should exclude the biggest danger your chickens will face on the ground. The biggest ground danger most of us face is a German Shepard or similar sized dog. Once you have created a citadel of sorts that will give you more leeway to design and build (or not) whatever style of runs, pens, or coops your little heart desires using that ever type of wire that your want.
IMHO, a Fort Knox style coop alone is an invitation to failure because you have
FIRST: allowed the vermin to access your poultry up close and personal.
And SECOND: because then you have no room for error. I've had good luck with a 1 inch mesh, 3 foot tall chicken wire fence with a 2 inch mesh 5 foot tall chicken wire fence topping it, for a total of a chicken wire fence 8 feet tall on Red Cedar fence posts. This enclosed an area of 3 acres.
Now I didn't fool around with predators, I relocated all the predators I shot, caught, captured, or trapped to an abandoned strip mine cut a few miles away. And with the K9 help on duty 24/7 it was indeed a brave fox or coon who took the chance to scope out my yard. Things like possums, mink, skunks, etc will happen because they are always looking for a home and have no, or zero caution. You also must remember that no one else in the community gave any chicken predator the time of day and that every young farm boy (and some of their sisters too) had a gunny sack full of steel traps and at least a .22 rifle to play Tom Bridger, Davy Crockett, or Annie Oakley with. Even 70 year old grannies were not above blasting a hawk out of the sky as I can personally attest to.