In my experience it is a good idea to have a safe place to put them if you have a problem. Even if you don't have a problem there just may be times you want them locked up. That extra flexibility can really reduce your stress levels when something happens.
Any kind of pen provides some protection, even just chicken wire. A large animal such as a big dog, a coyote, or old boar raccoon can tear most hardware cloth, let alone chicken wire. No wire is going to be perfect for everything. The size of the mesh holes matters, some critters like snakes, weasels or rats can get through some pretty small holes. How the wire is attached also makes a difference. Sometimes the connections are the weakness, not the material itself. The heavier the wire or the tighter the mesh the more expensive it usually is. There are always trade-offs.
I use a philosophy of a predator-resistant run during the day with a pretty predator-proof coop at night. Practically any of the predators can possibly attack during the day but the danger is usually greater at night. But I don't think that is your issue. I've seen bobcat, fox, coyote, and of course dogs hunting in the middle of the day. I ever trapped a raccoon around lunchtime so it was active. I think this is what you are concerned about, something hunting during the day. I have locked my chickens in the coop/run when I was free ranging them and lost one to a fox. I kept them locked up for a month so the fox learned there was not an easy free meal waiting for her. It worked. After a couple of dog attacks I switched from free ranging to electric netting. If you have a power source that might be less expensive than building a run. Some of that may depend on how many chickens so how big does it have to be. Electric netting won't stop hawks but it has stopped all ground predators for me.
My main run is fence posts with 2x4 welded wire fencing. I had enough spare material available so I covered most of it (tall enough I could walk under). I covered the rest with deer netting to stop a turkey from flying out. With my uneven ground I put an apron around it to stop critter from just pushing their way under, let alone digging. The 2x4 welded wire will stop any larger critter except a bear from getting in but snakes can get through. Baby chicks can walk through it.
I don't know what the right answer is for you. Some of that is your risk tolerance, some your budget, and some just which predator becomes a problem, if any. Good luck!
