I don't think there's ANYthing you "need". I mean, there are any number of chickens in the world that have neither coop nor run nor manmade feeder/waterer, and many of them live a respectable length of time.
It's just a matter of what you WANT.
If you want the run to be as secure as possible, hardwarecloth is a big help, particularly at "reach-through" height. Some people HAVE lost chickens to reach-through type incidents during the daytime, though certainly it isn't super common. If you want to use hardwarecloth for the whole thing, knock yourself out, although make sure it is attached and framed strongly enough; on the other hand, you don't lose MUCH security by using 1x1 or very heavy-gauge 2x2 or 2x4 wire (though beware, there are many flimsy garden type gauge wire meshes out there) or heavy-gauge well-installed chainlink. The things that can fit through those are *mostly* not daytime predators.
It comes down to personal choice, though.
FWIW, I use 1x1 or chainlink (and two runs have 2x4 wire on one end), with smaller mesh on the lower portions and a good solid roof on the runs. I am happy with it. YMMV though, everyone's different.
Good luck, have fun,
Pat