I will share some of my experiences and tips because we have a lot of the same predators. When I was building my coop and run I thought to myself "if I were a _______ how would I get a chicken dinner?" I used that basis to predator proof everything I could possibly find.
The coop: make sure that you use strong wood with the coop. I have seen evidence of raccoons pulling apart plywood like its nothing. Dogs will also be able to destroy any kind of flimsy wood if they work at it. Any ventilation areas should be covered with 1/2" hardware cloth. Raccoons can fit their hands through very small openings and can squeeze themselves through 4" gaps with ease. Possums can fit through smaller and snakes even smaller, of course. 1/2" hardware cloth IMO is the best because there is no predator (that I can think of) that can fit through it. 1" can fit most snakes and weasels and minks can fit through 1" gaps very easily. Do not use chicken wire for anything, if you were planning to.

the lock on the door is a good idea. I have a lock on my door too. It was mainly because a had a...problem.. With a certain individual thinking it was funny to come over and open my run in the middle of the night to let predators in my coop. It's also a good preventative for raccoons. They are very good with their hands and can figure out latches and handles.
The run: my run is chain-link dog fence that is buried. We used it for our coop/run because it was already there.

I am eventually planning on wrapping it in hardware cloth, so raccoons don't get tempted to stick their hands in and try and grab a bird. It's a very frequent occurrence for raccoons to do this. If your run is going to be stationary, I would cover the perimeter in a "skirt" of fencing to stop digging predators. A fox can dig just about anywhere it wants to and the best way to stop digging, is a horizontal barrier that they can't dig down further into. The sand is a very good idea! I've heard its easy to clean and doesn't smell as bad. It's very smart to cover the run, like you said for hawks. Or any climbing predator. I used wooden 2x4s and 1x1s to build a frame and covered my run. I am in the process of putting up a "circus tent" so when it starts snowing that Michigan snow, it slides right off and does to go into the run.
General: If you free range, make sure the chickens have plenty of cover they can go to if a predator comes by. It won't prevent an attack, but it will improve their odds of escaping. Make sure to never leave feed out to keep food thieves away and never leave the door open for any reason. I have not had a single predator get into my coop or run and kill any chickens since I Fort Knox'd it.
Just to see what it would do, I put a great horned owl statue on top of one of my coops and I haven't had any problems with rodents or wild birds.
Edited to add: because I remembered as I was posting... A good way to keep snakes out is collecting eggs multiple times or at least once a day so they don't have any snacks. Also make sure there's no places for them that would look like a good spot to hide under or go in.
