What kind of soil will you be starting with? What is your climate? Drainage issues?
I really don't know about chopping the hay. If you have access to leaves, they'd be the perfect litter. I'd do a combination of hay and leaves. There are so very many ways to go about reaching your gardening goals. You can break the bank with purchased soil and peat, or you can do a slow but sure approach: Traditional raised bed where you move amended soil from the paths to the growing beds, or lasagna gardening, or sheet composting, or permanent deep mulch, or Back to Eden, or Hugelkulture, or hay/straw bale gardening. Then you will be throwing chickens and the blessings they provide into the mix. The options are endless. I'm a fan of all of the methods I just mentioned: some, I use every year, I'm now experimenting with hugelkulture, and will be doing a Back to Eden orchard project this spring. The only type of gardening that I don't do and haven't done for over 30 years is the typical naked soil, tilled and fluffy with straight rows of veggies marching back and forth like well trained soldiers. I have a Troy-bilt sitting in my garage, and it only comes out to play when I'm busting up hard packed new ground.