How was it decided that there would be a lander and an orbiter? Were there proposals to do a "straight shot" (where all of the crew land on the moon in one craft)? What other ideas got tossed around?
Was the general design and mission outline used in the Apollo program already well-established when Kennedy announced the initiative to land on the moon, or was it invented by NASA in subsequent meetings? How did the "final product" differ (if at all) from the earliest ideas of the Apollo program?
Well there were three main proposals for the Moon Landing. Direct ascent, earth orbit rendezvous, and lunar orbit rendezvous, each with their own advantages and disadvantages.
Direct ascent would have been simple. One lander, one massive rocket. It would take off on Earth, go to the Moon, land, take off, and return. However, it would have been far heavier than the Saturn V, and would have needed the proposed Nova Rocket, which would have used eight of the F-1 rockets used by the Saturn V. Cost however, meant other options had to be considered.
Earth orbit rendezvous could have used weaker rockets. It would have launched a few ships into orbit, assembled them, and then directly flew to the Moon, landed, and returned, using one lander/orbiter. The benefit was that it was seen to be safer-no danger of marroned astronauts if they failed to dock with the command ship. It was also more expensive, and would have essentially built a space station on orbit in some instances.
Lunar orbit rendezvous was the method that was used, and was proposed as a cheaper alternative to Earth orbit. One powerful rocket would take a lander and an orbiter to the moon. The lander would detach and land, and only the orbiter would return to Earth. It had fuel savings because the lander could be made lighter, and not have to undergo the stresses of re-entry, and the orbiter wouldn't need to take the weight of the lander home. But it did carry the additional risk of needing to dock hundreds of thousands of miles away from earth, where no rescue mission or abort could be made. But it was cheaper, and only needed one powerful rocket.
After a few years of internal debate, LOR was chosen, despite significant internal opposition. Many studies refused to even consider LOR, until the lobbying efforts of John Houbolt-a NASA engineer at Langley-caused NASA to relent and consider LOR in their internal studies, and after a lot of debate, discussion and infighting, the darkhorse option of LOR was chosen in July 1962, due to opinion of many influential teams at NASA including Von Braun's rocket group in Huntsville, who concluded that LOR was the only option to reach the moon by the end of the decade.
I'm on my phone, but I can provide sources tonight, and I wrote my history BA on the space program so I've got a decent amount of insight.
EDIT: Sources! NASA has a good piece on the decision to choose Lunar Orbit Rendezvous online. http://www.nasa.gov/centers/langley/news/factsheets/Rendezvous.html
Most of my recollections about the N-1 rocket come from This New Ocean by William E. Burrows, which is an excellent history of space exploration, going from ancient history to the ISS.
Another excellent piece, which isn't really pertinent to most of the details here, but still a great read, is A Man on the Moon by Andrew Chaikin. Has a lot of great details from a slightly more personal side from the astronauts and NASA workers who took part in the Apollo program. It served as the basis for the HBO Miniseries From The Earth To The Moon, which is a must-watch.
Might also want to try on /r/Nasa