Tough assignment. You can get a very approximate answer to prop-rotor thrust and efficiency by comparing mv (momentum and thrust) with half m v squared (energy and power) for your chosen disc area. I think I saw a full analysis by von Karman.
An important practical challenge is sorting out the blade twist, which is a compromise between hover and forward flight.
Sorry, can't help any more, way beyond my primitive academic level!
PS - here's a comparison chart I did many years ago, not sure how accurate it is:
