4) No Space Shuttle. Rockets all the way. (Why mess with something that works)
We would have a space shuttle. It simply wouldn't be the "jack of all trades, master of none" we got.
The space shuttle was supposed to be a lightweight launch craft for transporting people to/from LEO where they could rendezvous with a space station and take a transport to a location like the moon. Economically, it made a lot of sense. It would have been fairly simple, cheap to operate, and with fewer disposable parts than the Saturn V. (Which basically throws away millions of pounds of hardware to return barely a few tons of mass. Very wasteful.)
So what went wrong?
Obviously, the same politics that killed the moon program. Nixon told NASA that they could have one launch vehicle, and the Saturn V was too expensive to be "it". Oh, and they needed to meet the military's needs for a launch vehicle as well, because the Titan rockets were also too expensive.
NASA got out their abacuses, ran some numbers, decided that the shuttle was key to a future space station, and committed to producing a super-shuttle that could be all things to all people. After all, they had the technology, right? Right?
Well, sort of. The engineers did an amazing job of producing the most sophisticated piece of space equipment ever designed. The power curves were incredible and the engines left the Saturn V in the dust. Only problem: It was a hellva lot of mass to send up and bring back, leaving little room for cargo. Worse yet, it was so complex that maintenance costs were through the roof. In the end, it would have been cheaper to continue operating the Saturn V with the economics of scale resulting in MORE cost reductions than the Shuttle ever realized!
What I'm getting at is that if we're going to play along with this dream-world where politics don't kill off programs, we'd have the Saturn V, the space shuttle, the space station (with artificial gravity!), and transport tugs originally envisioned by NASA. Because all those pieces have to fit together to make this mythical lunar base of 5,000 people possible.
Back here in reality, all those ideas were doomed from the beginning. The politicians only ever supported the space program to combat the USSR. By the 1970's, the Soviet Union had already collapsed. They were just coasting on momentum from there on out. That's why (save for a push by Regan to push the USSR to the brink of bankruptcy) the space program never recovered. There was no political need. And anyone who knows anything about politics knows that there has to be a need commiserate with size of the solution before there will be a large commitment. Hopes, dreams, and peaceful exploration ala Star Trek just don't cut it. :-(