It will house just 4 chickens, and will be behind our garage.

My thinking is something like this one, but the run will be perpendicular to the coop, making it an L:

The garage has a 4' eave in the back, so the house and part of the run will be sheltered. Outside the coop, I'll run a fence from the back of our garage to our yard fence, giving them an approximately 15' x 20' area to roam in when we don't let them run around the entire back yard.

I'd appreciate any advice.