Most important is that your run have good drainage.
Either/or to keep water from flowing in and puddling and also so it can flow back out of the run area.
A few inches of coarse wood chippings(from a tree trimmer) can work well in all climates. Helps to have a place to store the huge pile they dump.
What kind of bedding you use may depend on how you manage the manure.
This is about cleaning, but covers my big picture
-I use poop boards under roosts with thin(<1/2") layer of sand/PDZ mix, sifted daily(takes 5-10mins) into bucket going to friends compost.
-Scrape big or wet poops off roost and ramps as needed.
- Large flake pine shavings on coop floor, add some occasionally, totally changed out once or twice a year, old shavings added to run.
- My runs have semi-deep litter(cold composting), never clean anything out, just add smaller dry materials on occasion, add larger wood chippings as needed.
Aged
ramial wood chippings are best IMO.
-Nests are bedded with straw, add some occasionally, change out if needed(broken egg).
There is no odor, unless a fresh cecal has been dropped and when I open the bucket to add more poop.
That's how I keep it 'clean', have not found any reason to clean 'deeper' in 10+ years.