Once the chickens have destroyed all the green stuff in their new run and turned it into a barren wasteland putting down a lot of dry organic material keeps the run free of mud and odor. The chickens will happily spend time scratching through the litter looking for bugs, etc.
A nice mix of wood chips, pine straw, dried lawn clippings, leaves, etc. gives them a substrate that resembles a forest floor (you'll have a head start since you're beginning with genuine forest floor) -- the perfect habit for chickens because they are native to the forest floor in southeast Asia.
I find that I *can* use straw in limited quantities as long as it's mixed with other materials.
In fact, I consider a mix of materials superior to any one material used alone. The diversity of materials and textures reduces the tendency to pack and mat. If I see a spot that is in danger of becoming compacted I toss a handful of scratch there and the chickens do the work of fluffing it up.