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Good questions. You will probably get a lot of different opinions on this since we all have different conditions, different management practices, and different risk tolerances. Some things will take care of some predators but not all. Snakes, weasels, and rats are real hard to protect against. Your weather can make a difference too, not just heat and cold but rain too.
For my coop, I enclosed the end of a shed, winding up with an 8' x 12'. I used a 4x4 treated timber for the sill of the one wall I had to build, used 2x4's for the framing, and T-111 or 3/8" plywood for the walls, depending on what I had. For ventilation, I left the area under the overhang open and covered it with 14 gauge 1" hardware cloth. A lot of people use washers and screws to attach the hardware cloth. I used strips of 1/2" thick wood and screwed that over the edges of the hardware cloth, making sure the screws go through the openings in the hardware cloth. I think I get a stronger connection this way plus the sharp edges of the hardware cloth are covered up. There are many different ways to do this.
For the run, I set wooden posts on 8' centers and stretched five foot wide 2"x4" welded wire on that. Around the bottom of the welded wire, I put 24" chicken wire, putting it about 18" high to prevent the chickens from reaching through fro grass and exposing their necks to any predators around and stopping a raccoon from reaching through to grab chicken parts. I bent the other 6" of the chicken wire as an apron to slow down some predators from being able to just wiggle under the fence. I know it won't stop a serious predator, but I have also seen a possum just sort of walk/crawl under a fence that was pretty tight to the ground. The chicken wire also keeps baby chicks from being able to walk through the fence and get away from Mama's protection.
Due to a 70 mph straight line wind taking the roof off a shed, I had some metal for a roof over most of my 12' x 32' run. I still have about 8 feet that is not covered. The metal roof helps keep the run dry, provides shade, gives me a dry place to feed outdoors, and deters the hawks. I enclosed the area from the top of my fence to the bottom of the roof with welded wire. That keeps the chickens from flying out (some pullets were getting out trying to get away from an amorous rooster) and it slows things down from climbing in. On the part that is not covered, I attached welded wire so it is sticking straight up, no brace at the top. Since there is no brace at the top for them to land on, the chickens do not try to fly up there. Also, since it is not supported, anything that tries to climb up there will bend the wire back over itself and should have real trouble getting in.
Around the coop, I took either 2"x4" welded wire or hardware cloth, whatever I had left over, and put an 18" apron, horizontal to the ground. The idea is that a predator tries to dig under the coop wall, hits the wire, and does not know to back up. I did not bury it, but many people remove about 2" of the sod then put that back over the wire, hiding it. Grass grew through mine and the chickens scratched enough dirt up on it to hide most of it. I don't have any problems mowing or weed eating around it.
For hardware, make sure you use something big enough. You want hinges and such strong enough that a raccoon or coyote cannot rip it off. I use snap locks and carabiners to hold the hasps closed. Raccoons could probably figure them out, but they have not yet and I have trapped raccoons in the area. Make sure you get your hasp is big enough that the snap lock or carabiner can fit through the hole.
My philosophy was to make the run predator resistant and the coop predator safe. I let mine free range most of the time but sometimes leave them locked in the run during daytime. At night, when predators are most active, they are locked up safe in the coop. I'm not fully protected against snakes, rats, and weasels, but these are normally not a threat to grown chickens. (I know, it depends on which member of the weasel family you have) They will eat eggs and baby chicks, so there is some risk.
I just saw Woodmort's post. Those heavy staples he is talking about are not the staples you use to put a report together. He is talking about the fencing staples that you drive in with a hammer. I used 1-1/4" or 1-1/8" fencing staples, can't remember exactly which size. Some people get confused about that.
Hope this helps. Good luck.
editted to add. I forgot to mention. I use J-clips to make wire to wire connections, where I have to butt wire up to other wire. This is good to attach an apron or connect one roll of wire to another when building a fence. It requires a special tool for this this. Some people use hog rings. Either can work. J-clips and the tool can be found in the rabbit section at
Tractor Supply. This is what is usually used to build rabbit cages.
