My coop has a wood floor and I keep about a 6" layer of pine shavings in there at all times. About twice a year I dig out all the shavings and add them to my manure pile, then replace them with fresh shavings. I never find any wet spots when I do this, so I am thinking 6" is deep enough to protect the wood of the floor from damage. I've been using this system for over 4 years now and never have an odor or fly problem.
Out in the run I use sand because in this area the soil is all clay, so the sand helps break up the clay and promotes better drainage. After a heavy rain I do have a few puddles, but they do drain away quickly. When I first built the run, I used about 2 yards of construction grade sand from Home Depot and now I just top it off with an occasional bag of sand in any consistently wet spots. That seems to dry them right up.
HTH
Rusty