The 2x8's are probably overkill but would work. 3/4" plywood for siding is also overkill but would work if it's exterior grade. Definitely would prime and paint all the edges before putting it up and caulk the heck out of it and prime and paint the exterior. Might be a good idea to actually cover the seams with trim boards aka board and baton type look. As far as locations go, all of the places you have marked are too far away from the house for my liking. Much of the enjoyment of chicken keeping is being able to watch them. You'll also need to go out to the coop at least once and likely more times per day so fairly close proximity to the house is a good thing. I want to be able to do something right away if I hear a commotion in the coop or run. Personally, I could not imagine keeping the chickens in a place that I couldn't easily see and hear even though I know people do it. Just food for thought.
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