Be aware that it's usually only called "hardware cloth" at the 1/4x1/4" and 1/2x1/2" sizes. Anything larger, even 1/2x1", is generally called "welded wire mesh" or something similar; the smaller part of that range can also be called "cage wire" (up to, like, 1x2"-ish).
If a store does not have the size mesh you want to use, ASK. A lot of times they can order it for you, as long as you want a full roll or more. Don't forget to ask at feedstores too, not just hardware stores.
What size you want to use depends on what your goal is. GOOD QUALITY heavy gauge 2x4" wire will keep dogs and raccoons and other large animals from going thru it, but will admit weasels, minks, smaller skunks, baby coons/possums, and the ARMS of adult raccoons; it also lets chicken heads out and chicks can pop thru it.
If you use 2x4" wire, it'd be wise to put something smaller mesh along the lower portion of the fence and anywhere else within raccoon's-reach of a chicken, and shut the chickens in a secure coop at night.
Smaller mesh e.g. 1x1" welded wire will admit only the smallest weasels and raccoon arms (and banty chicks can pop out); personally I'd want the chickens shut indoors at night if the run was that size mesh, and if reach-thru seemed likely would also add something smaller mesh along the bottom portion of the fence.
It just depends on what you're trying to achieve and how much you're willing to spend to achieve it. Do beware of flimsy yard-and-garden-grade fencing which is too thin and too poorly welded to stand up to assault by hungry animals.
Good luck, have fun,
Pat