There are a lot of factors involved, like are you in or out of the city? What type of predators are in your area? Cats and dogs? Raccoons and skunks? Coyotes and hawks? Bears and mountain lions?
Ultimately you want to protect from digging predators (bury 1/2 inch hardware cloth 2feet below ground surface), climbing and bomb diving predators (roof and/or chicken wire/ hardware cloth over the run). And grabby/pushing predators that can reach through chain link fences (wrap run in hardware cloth).
My neighbors let their girls free range and only have a loading shed for shelter. I on the other hand have a locking coop for nighttime safety, run walls built with chain link fencing wrapped in hardware cloth to stop raccoons, snakes, and mice, clear and metal corrugated roofing for sun, cat, and hawk protection. And buried hardware cloth for the coyotes and my in-law’s rambunctious dog.
I do not worry about bears or mountain lions.