Re-doing my 800 sq-ft lawn in Phoenix AZ. What's the best process to have a level, nutritious lawn for seed?

Soak the soil. I live in Phoenix too, and whenever I have to dig, I cut a shallow trench (I usually only ever have to dig trenches) a couple inches down and fill it with water. When the water settles through the soil, it will soften it, so you can dig fairly easily by hand. Also the water settling will help to level it out. Go to H.D. and pick up a bunch of bags of steer manure. It's cheap and good. If you want free manure, go to a horse farmer. Till it into the soil. You don't need to till very deep for gr. Use the perennial Rye for your winter lawn. It's more expensive, and not as fine as the annual, but you'll save money with reseeding next year.