That will not be very predator proof. Hardware cloth is good, but only if it's attached firmly at all edges. Just pounding posts into the ground will allow things to go under or over it. Or a dog might just knock it down or stretch it out of shape and get through.
If you're just going to run something between posts to contain the chickens (not predator proof) then chicken wire is as good as hardware cloth.
If you want something sturdier but fairly simple: maybe a dog kennel? They tend to have large holes, which may need to be covered with hardware coth, but they are sturdy enough to keep a dog or raccoon out (raccoon could reach through, but not go through.) Some even have roofs. (I'm thinking the kind that are 8x8 feet, or 10x10, or 5x10, or something like that.)
The dog kennels are not the absolute cheapest choice, but they often come apart into panels that can be moved or re-purposed later; and they are the sort of thing people are used to seeing in backyards.
Is this going to be inside an existing fence? The main daytime predator would be domestic dogs or hawks, while most other wild predators come at night. So dog-proof run by day (existing fence or something you put up) with a cover because of hawks (the bird netting roof you mentioned--also keeps the chickens from flying out) and a more secure coop by night usually works out fairly well.