The best stuff about Neil Armstrong doesn't seem to get much press. The reason he was selected to land the LEM was he was the best pilot in the stationary simulator down at Houston (hilariously electro-mechanical/analog) and with the LEM Simulator, which was basically a flying bedstand. No wings or lift surfaces, just a giant jet engine that pointed straight down. You kept it upright by using the same retrorocket controls that the LEM had. The jet engine was keyed to generate exactly enough thrust to offset 5/6 of earth's gravity, in other words, simulating lunar gravity. Apparently, Armstrong was the only one who could fly it.
On their final approach to Tranquility Base, the autopilot began freaking out. Compensating for the difference beteween the altitude reading from the radar altimeter and the telemetery from Houston, the computer freaked out (it only had 2K of memory). Working with the coders on the ground, Buzz Aldrin patched the autopilot program and got the AP back online. Only now they were running out of fuel. And the LEM was headed for a collision with a massive boulder that hadn't shown up on the survellance photos.
Armstrong looked out through the rangefinder and picked out a good landing site. He and Aldrin did some fast math on their pocket slide rules (no calculators). Then he flipped off the computer and landed the bird by feel. They travel 300,000km from the Earth, with every millimeter of the trip planned out by the most powerful computers available, and then Armstrong lands it by the seat of his pants. To me, their teamwork and fast thinking are more impressive than being the first guy out the door.