We are in the process of covering all of our 16x8 run. I can't wait! The part of the run that isn't covered now doesn't get used at all in the rain. The base of the run is river silt and on top is a layer of wood chips and fir nuggets. So far that has been working. It decomposes over time and turns into a mulch that you can use in your garden. I put a fresh layer on as needed and try to rake it a bit everyday. It seems to drain well, but in the rain we get around here it's still damp. The girls are able to dig and take dust baths as long as it's dry. In the coop I put down a dusting of DE and Sweet PDZ (Zeolite) then a mix of 80% pine shavings to 20% bedding pellets with Zeolite. It keeps the coop nice and dry. I use one of those doggie poo shovel set ups to pick up obvious poo and make sure to stir things around so any damp spots dry out quickly. In your case you could probably use a cat box scoop to do quick clean-ups and stir things around. In my mind the dryer the better to keep healthy birds. One thing you might really like is using a water bottle with a screw in poultry water nipple http://www.amazon.com/OOOUSE-Nipple-Drinker-Chicken-Poultry/dp/B00CIJENP4/ref=sr_1_5?ie=UTF8&qid=1446668300&sr=8-5&keywords=poultry+water+nipples I will try to post a pic of the water bottle my husband put together for inside the coop. You would probably need 2 for your run. Then you don't have to worry about water being tipped over or getting dirty. In the run I use a 5 gal. bucket with water nipples on the bottom. On Amazon you can get a 2.5 quart bucket waterer. I don't see a lid though. It would need a lid for sure. http://www.amazon.com/2-5-Quart-Chicken-Poultry-waterer/dp/B004U2F2DO/ref=sr_1_6?ie=UTF8&qid=1446668559&sr=8-6&keywords=poultry+water+bucket Of course you have to be able to hang it, but they are awesome!!!!
Our coop and run have evolved since it was first built. There were a lot of things I didn't anticipate. You'll figure out what works best for you. It always seems like I learn something new.