I would say that if you aren't worried about predators, chicken wire is fine. But go look at the construction stucco wire before you buy the roll of chicken wire. It is the sme thing but the construction wire is thicker, taller, and easier to handle. And cheaper!!!
I would put chicken wire on the run, but hardware wire on openings to the coop. Most predators will try to get your flock during the night, so if they are especially protected then, the better. But as in all things, it really depends on your risk aversion and personal situation.