I had a covered run with a rock/dirt floor. I used some pine shavings, but mostly detritus from around the yard(leaves, grass clippings, etc.). Our run was in the space under our sunroom, and we used mobile fencing when we wanted to confine them to the run, so it was easier to facilitate movement of the bedding.
My run is all grass and 3,000 sq ft... My coop I use pine shavings or straw depends on my mood I guess. If I want to take a trip to the local farm, I do straw. If not I go to TSC and get pine shavings.
I do deep litter, mainly chunky aged wood chips with dried leaves and dried grass when available. Our run is not roofed and we get a lot of rain during fall and spring so the deep litter lets the water drain through.