Have the coop, need the run, expert advice needed ;)

Well, I had a big great description typed out, about to hit send and my lovely 8 yr old hit the @#%& power button while digging for paper. AGH

Ok, so I have a coop, set up pretty good I think. Happy with it so far. And by so far, I mean I am a first timer at chickens and they are 10 days old HAHA

But the coop is 12X8 and 8' tall, with a 10' vault, insulated, 2 human doors, 3 windows (up high) and a automatic solar/ photo eye sensor chicken door. About to build the boxes and roosts, and after looking at the other posts - we will make sure to bolt everything to the walls and have nothing attached to the floor. My only regret thus far is not wiring it - however, I can always run power to it later, and I think I probably will. My chicks are out there now, I have an extension cord for the heat lamp and radio going

We live in the woods.
The run will be in the woods.
I can fence in as much as I need, we have acres upon acres.
I have 26 chicks, could probably handle 10 or so more, may or may not.
How big should I make the run?
Any MUST haves?
MUST NOT do's?

My neighbors have chickens. Have for a few years now. They have not had predator problems until the last summer, a fox perhaps, got in the run at night, the one night she did not lock them up in the coop, and drug off a hen. They set out live animal traps, and only trapped a few opossums.

I have a small dog, who runs the property, and a cat, who is bigger than the dog lol and kills moles.

I have not seen hawks up here (but plenty in the county!), plenty of crows here, hoot owls, deer.. I saw fox families up until about 2 yrs ago, haven't seen them in a while. Coyotes, off in the distance, bob cat, in the distance.. Nothing comes close to the house. The coop in about 30- 50 feet from the house. The dog barks at all critters.

So, whats my best bet, so keep the girls safe? The coop is definitely critter tight, something would have to chew as if they were chewing into a house to get in, and the auto door will shut them up after sunset.. so they should be fine in there.. right? So for the run, what are your expert thoughts and opinions?

 

haha, Well, they like country. They don't like pop or rock. Occasionally I put on classical. I want smart chickies. HAHA

 

How deep do you bury the fencing? We were gonna have the boys start trenching it soon.. haha good chore for them! We werent going to cover it, as it was a pain in the butt to walk into my neighbors run all hunched over, they will be locked up at night, would covering it be necessary you think? Whats the best way to do it? There are lots of trees in the area we will fence for the run.