The authoritative source of dates is The Apollo Spacecraft: A Chronology. Volume I (of the 4 volumes) ends at the spacecraft mode decision, which is what you are asking about. Volumes II and III are smaller design decisions. Volume IV starts with the Apollo 1 fire, and ends at the end of the program.
Looking at the key events page:
1957 October 4: Sputnik I, the first man-made satellite, successfully launched by the Soviet Union.
1958 October 1: NASA officially constituted and charged with responsibility for the U.S. civilian space program.
1960 January 28: NASA's Ten-Year Plan presented to Congress during testimony before the House Committee on Science and Astronautics. (includes landing on the moon in 1970)
1960 July 28-29: The announcement of the Apollo program to representatives of American industry.
1960 September 1: The Apollo Project Office formed under the Space Task Group (STG) Flight Systems Division.
February 7: Final report of the Low Committee outlining a manned lunar landing within the decade using either the earth orbit rendezvous or direct ascent technique.
1961 April 12: First successful manned orbital flight, by Cosmonaut Yuri A. Gagarin of the Soviet Union.
1961 May 5: First successful American suborbital flight, by Astronaut Alan B. Shepard, Jr.
1961 May 5: Completion of the first draft of the Apollo spacecraft specifications by STG.
1961 May 25: President John F. Kennedy's proposal to Congress and the nation of an accelerated space program including a manned lunar landing within the decade.
1961 June 10: Report of the Lundin Committee recommending a low-altitude earth orbit rendezvous mode using the Saturn C-3 to accomplish the manned lunar landing mission. (didn't happen that way)
1961 August: Report of the Heaton Committee recommending the earth orbit rendezvous technique and use of the Saturn C-4 for the manned lunar landing mission. (not that way either)
1961 November 20: Report of the Rosen working group to the NASA Office of Manned Space Flight, recommending direct ascent as the primary lunar landing mission mode with a backup rendezvous capability development. (nope, not that)
1961 November 28: Selection of North American Aviation, Inc., as principal contractor for the Apollo spacecraft under MSC direction.
1962 July 11: Selection by NASA of the lunar orbit rendezvous mode for the manned lunar landing mission.
1962 November 7: Selection of the Grumman Aircraft Engineering Corporation by NASA to design and develop the lunar excursion module under MSC direction.
The specific entry for July 11, 1962 is as follows:
NASA officials announced at a Washington, D.C., press conference that the lunar orbit rendezvous (LOR) technique had been selected as the primary method of accomplishing the lunar landing mission. The launch vehicle would be the Saturn C-5, with the smaller two-stage Saturn C-1B (S-IVB as second stage) used in early earth orbital spacecraft qualification flights. Requests for industrial proposals would be issued immediately on the lunar excursion module, The reasons for the decision on lunar orbit rendezvous were explained:
A higher probability of mission success with essentially equal mission safety was provided by this technique.
- The method promised mission success some months earlier than other modes.
- LOR costs would be ten to 15 percent less than other techniques.
- LOR would require the least amount of technical development beyond existing commitments while advancing significantly the national technology.
In addition, it was announced that:
- Studies would continue on the feasibility of using the Saturn C-5 to launch a two-man spacecraft in a direct ascent approach to the moon or in an earth orbit rendezvous mode.
- An in-depth study would be made on a lunar logistics vehicle.
- Investigations would continue on the development of the Nova launch vehicle.