May I make a suggestion? As long as you're in the process of building your coop and run, now is a good time to consider alternatives. Have you thought about, not just putting wire mesh over the top of the run, covering the run so that rain, snow, and wild bird droppings can't get in?
When I built my run four years ago, I put poultry mesh over the top to keep the chickens in and wild things out. But I quickly found out that they needed shade as well as shelter from rain and snow. Also, I found out very soon just how horrible a run smells when it gets wet!
I used 2" x 4's on the long sides, and then I ran 1" x 2's perpendicular to those at three foot intervals. Then I screwed translucent fiberglass panels over that frame. I used green panels in some places for shade and transparent ones over the rest of the pen to allow maximum light. I'm very pleased with it. I recommend it highly.
Recently I added a new pen, and in the days before I got the roofing finished, the chickens avoided that pen. As soon as I put up the roofing, they happily began to use it. It dawned on me that chickens are a lot more comfortable under cover.