Two main ways of getting Manned crew to Mars.
1) build large rocket- Saturn V or larger.
2) Assemble in orbit.

Either of these ways you could get to Mars with shorter travel time if you spent less payload weight on creating artifical gravity for crew and more on booster and smaller payload.
You would also do everything to reduce payload further (no gardens, etc) and put everything you can on the ship which is carrying the cargo (requiring 9-12 months to get to Mars).

Going to the Moon first isn't really relevent to this particular point (other than that is the approach I would favor and it would start trip to Mars from higher up in Earth's gravity well- compared to assembling in LEO).