I wrote an article on this: https://www.backyardchickens.com/articles/using-deep-bedding-in-a-small-coop.76343/
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I have a spacious run with several bushes growing inside. The stagnating water (after lots of rainfall) is taken care for.You are correct - keeping things dry helps control odours, flies and keeps livestock healthy. I have 10 beasties 9 weeks and 19 weeks.
I personally use wood shavings (same as I use with the horses) and I 'pick' out the Hen House a few times a week. My kiddos are spoilt for space, they have the whole barn during the day (30x60 10 stall barn) and a fenced in area about 15' x 50' which is grassy. The critter-kids only go into the Hen House at night so easy to clean.
I do not use old lawn clippings, or shavings outside, this would only get mucky and muddy when it rains. Keep it dry, remove manure frequently and you won't have odour, or flies and the kiddos will be happy and healthy.
Wish I could get chopped straw here for the horses, I see it sometimes but it just isn't popular with the Horse Community here. A few stables use chopped Flax chaff for bedding but again not easy to get and very expensive.I use chopped straw. it's warm in the winter and cool in the summer (depending how deep you lay it in. It's also very easy to clean up. Also, when you clean your coop, just spread it and dig it into your garden (early spring or late fall). I tried white pine chips, and they were ok, but took forever to compost. I like the biodegradable properties of straw. Chop straw come in compacted bales and is easier to handle and lay down in your coop. It can be bought at most any feed store.