I'd let them tear up and eat all the grass first, chickens love that. Then when they've demolished the grass in the run, add wood chips. you can mix them with grass clippings, old leaves, garden weeds, etc, and the chickens will love scratching around as the wood chips cold compost the poop. Look up Deep Litter and Deep Bedding on this site. One allows water and actually helps cold compost the poop the other keeps the poop dry in the coop, and you change it out about 1-2x a year. Also consider if you'd like to do poop boards with zeolite (sweet pdz horse stall refresher granules). This will keep your coop bedding cleaner, but require a bit more daily work from you. There are threads on this site about poop boards and zeolite/sweet PDZ also.
I love your coop and run! They are awesome and I am jealous of your setup!!!
Make sure you do your research on what predators are in your area - there's a Forum on here that might be helpful. Depending on what else you have going on (your own livestock dogs, electric fencing, etc) and what predators you actually have in your area, the 1"x2" wire can be sufficient, but there are a number of predators that can enter anything larger than 1/2". Also, I'd put some wood trim over anywhere you've stapled the 1"x2" wire in place - racoons can grab the fencing fabric and rip out staples, so covering them with trim is helpful to prevent that. Mink and weasels can get through 1"x2" I think, but these may or may not be an issue in your area while racoons are pretty much everywhere.
If you have or put up any roosts in the run that touch the run walls, make sure you put a piece of plywood or metal, or 1/2" hardware cloth along the run wall to protect the area where chickens will be roosting/resting/sleeping. Imagine a racoon reaching through the run wall, and how long their arms are and where they can reach to, and that's the area I would block off around the end of the chicken's roost. Racoons will reach through 1"x2" wire and pull off chickens heads when they're asleep or any time they can reach them. Many folks will put a couple feet of 1/2" hardware cloth along the sides of the run right at the bottom edge, so the hardware cloth goes from the ground up the side wall of the run about 2 feet when using 1"x2" fencing, since the chickens walk around on the ground, the 2 feet tall 1/2" hardware cloth will prevent racoons reaching through to grab them during the day also.
Best of luck and I love your coop!!!