The mode that Apollo would use to land on the moon was the most studied, analyzed, and debated decision made for the lunar landing program. There were four main choices Direct-ascent, Earth-Orbit Rendezvous, Lunar-Orbit Rendezvous, and Lunar Surface Rendezvous.
This brings us to Project Gemini. Gemini started after Apollo had begun, in part to answer a crucial question for Apollo. Was rendezvous and docking in orbit a feasible basis for a manned lunar landing mission?