If you ask people what were the first words spoken by a human from the moon's surface, their answer will often be Neil Armstrong's "One small step" quotation. I happened to think about that a bit today, and it doesn't really ring true.
As of yet, no human being has truly been in contact with the lunar surface. The only way such an event would truly be possible would be to build a pressurized enclosure on the moon. Only then could someone walk on the surface without the protection of a space suit. What we're left with is an approximation - the Apollo astronauts who visited the lunar surface did so constantly surrounded by a bubble of Earth's atmosphere, whether that bubble was located around them in a suit while they were EVA or whether that bubble was around them in the LEM. And Neil Armstrong and Buzz Aldrin spent an extended period of time after the actual landing before they opened the hatch and descended to the actual lunar surface. Buzz even had rime to take communion.
So how do you pick the first words spoken from the moon? Well, they'd have to be the first words spoken by a human being who was inside of a vessel that was in contact with the lunar surface. And if you read the NASA transcripts of Apollo 11, you'll find that the first words from the lunar surface given that definition actually came from Buzz Aldrin.
As the LEM was descending for its final landing, a probe descending from one of the landing legs made contact with the lunar surface. That probe lit a light on the instrument panel. When that light lit up, Buzz said, "Contact light," as a cue to Neil to cut the engines and let the LEM fall the rest of the way to the surface.
And those words were the ones that made history.
History is often like that. The first creatures ever to cross the Golden Gate other than by water or air were a pair of workmen on the Golden Gate bridge who were engaging in a repair mission of sorts. They hauled themselves over the unfinished cables and into the history books more than a year before the first pedestrian would cross the finished bridge. The flag raising at Mount Suribachi (on Iwo Jima) that was widely and famously photographed was actually the raising of the second flag, ordered by a commander who thought the first flag was too small. If you visit the Amundsen-Scott South Pole station, you'll find two poles - the real South Pole, which is just a simple spike in the ground and a small, plain sign, and a few hundred yards away, is the so-called "ceremonial" pole, which is a giant barber-pole decorated monstrosity surrounded by the flags of all the nations with a presence in Antarctica. The ceremonial one is the one that people expect to see, but it's not the real one.