A three-person crew? (What happened to the dreams of yesteryear? Von Braun wanted to send a fleet
to Mars to begin building a colony.)
How about establishing a Moonbase first, even a small one. It would serve as the perfect testing ground for the many technologies we need for long duration spaceflight—including the opportunity to test new engines. The Moon is also close enough to abort back to Earth in the event of catastrophic failures in the "colony."
To borrow a phrase from Arthur C. Clarke, there is little purpose in "brief reconnaissance raids." It's not the 1950s or '60s anymore. We don't need space spectaculars just to prove that we can do it, perhaps before the other guy. "Long duration" missions should be a preface to permanent bases. They should be more than stunts, or rock gathering field trips.
The "men are better than machines" argument is no longer tenable considering the current sophistication of robotics. Sending people is much, Much, MUCH more expensive.
I believe private investors will build the first bases and then colonies on the Moon, Mars and perhaps elsewhere in the Solar system—if they can evade being nationalized and then looted by the parasitic governments of the world.