I wonder if the currently feasible most interesting manned trip wouldn't go this way:

A launcher (like the Ariane 5, or the Zenit or the Proton or the Atlas 5 or Delta 4) sends a capsule (with x astronauts depending on the capacity) into Translunar Injection and it goes around the Moon in a free return trajectory, returns back to Earth.
It would last no more than 7 days.

After TLI, there would hardly be any further need to use more fuel (no moon orbit nor moon landing) except for corrections.

If the flyby behind the Moon takes place when the Moon is at its apogee, it means that the spacecraft could achieve the absolute distance and speed records at the same time.
Those records can be rewarded by some kind of Prize similar to the X Prize to encourage private companies in doing it.

It could become some kind of sport event (speed and distance) or the ultimate possible space trip.

The experience of viewing the Earth from so far, if repeated and shared, is something we haven't seen since the Apollo era.

Raoul