You can start with a few inches of shavings - 4-6" or so to begin with. I have a pine shaving base but have dried leaves and dried pine needles mixed in. I also grow herbs for my chickens and will occasionally toss a handful of various herbs (lavender, marigold, basil, various mints, lemon balm, lemon thyme, cinnamon basil, lemon balm, jasmine bee balm, and some squash blossoms when I have them in the garden - sometimes some nasturtium, rose pedals and native flowers and plants - dandelion, clover blossoms) - the chickens dig around searching for the herbs to eat, which helps the bedding and they also put a nice scent in the coop and nesting boxes (although with DLM you shouldn't have a bad odor) - the various herbs and flowers have various nutritional benefits as well.
I compost in my run, with a wood chip base and the same mix of pine needles, dried leaves, grass clippings, etc. Often, when it comes time to clean out the DLM in the coop, I add it to the run (either mix it into the run mix, or use it to replace what I may be removing from the run for garden needs). In the rare event that my run couldn't handle the DLM from the coop, I'd add it to my other compost bins, but with DLM only getting a couple of cleanings annually, this usually isn't an issue.