I started off with a nice grassy chicken run. In a few months, the chickens had ripped up everything and there was nothing left but dirt. At that point, I dumped a trailer load of wood chips I got from free from our county landfill. That works great and the wood chips looked very nice.
Over time, I ended up turning my chicken run into a chicken run composting system. I now bag all my grass clippings and dump them in the run. The chickens eat fresh grass clippings and love to scratch around in the clippings looking for bugs to eat. In the fall, I dumped all my leaves into the chicken run. The chickens loved playing in the pile of leaves. They mix all the wood chips, grass clippings, and leaves together making an excellent compost in place setup.
I also throw just about anything organic into the chicken run, like weeds pulled from the lawn and garden (no pesticides on my lawn). I will just throw all our kitchen scraps right on top of the chicken run compost material. The chickens will eat most of the kitchen scraps, and the rest just gets composted with everything else.
I only have bird netting on top of my chicken run, so everything gets wet when it rains. That is what makes the composting possible. I don't know how well it would work if you had a solid rainproof roof over the material in the run.
I use dry deep bedding in the coop. For the past couple of years I used free wood chips, and that worked great for me. This winter, I used paper shreds I make at home and that has worked out just as good. I advocate using any litter material that you can get for free and that can be composted when you clean out the coop. In my case, I take out all the old coop deep bedding twice a year and dump it out in the chicken run for composting.
The magic is in the coop deep bedding system, as it automagically absorbs the chicken poo and keeps everything looking clean and smelling fresh. The chickens will naturally turn over the bedding in the coop, but if you need more turning action in an area, just throw some chicken scratch on that spot and the chickens will scratch and peck that area for you, turning the bedding, which refreshes everything.
I only clean out my coop deep bedding twice a year, and I could probably easily get by with maybe only once a year if I wanted. When I used sand, years ago, I was constantly cleaning the coop at least weekly. Personally, I would never go back to using sand - and I live on a lake. Sand works, but it requires a lot more maintenance than the deep bedding material I currently use.