The depth of embedment doesn't really control the design approach - the deep pier/caisson references should give you what you have asked for in this thread.
Shallow foundations pose special problems, though. How deep is the "zone of moisture influence" in your area? What is the accepted local practice? What about expansive clays? Collapsible soils? Liquefaction? Slope stability concerns? (Local issues not included in this laundry list?)
Often the design calculations to size the foundation represents the easy part!