I started with about 8 inches of wood chips from a tree trimming company. On top of that I dumped a couple of inches of pine shavings and chopped straw. Then I added some shredded leaves and partially composted lawn waste that I dug out from under the snow.
I started my deep litter in early April and it limited what materials I could get. The tree guy couldn't figure out what I was planning to do with the chips considering all of New England was still under feet of snow. If I could have gotten grass clippings I would have used them. All summer long I did add clippings to the run. Any chicken-safe weeds and garden clippings go in the run. I gather my leaves in the autumn with the bagging mower and I just dump them in the run.