Of the 3,000 people polled by Sony Bravia, more than half said that Armstrong becoming the first man to walk on the moon was their highlight, while 37.5% opted for the election of Barack Obama as the first African American president.
In third place was the 1963 assassination of President John F. Kennedy, which was named by 27% in the survey.
Sony's Christian Brown said: "The nation favours 'World First' television moments that have either a visual impact or create a poignant piece of history - moments such as the first man walking on the moon and President Obama's recent inauguration."
Filmmaker Tal Rosner has been hired by Sony to produce a short film comprising memorable TV firsts.
"I wanted the film to be inspiring. I would have loved to have included Obama being elected or inaugurated, that would have fitted," he said. "I didn't want to choose the most obvious ones. Instead of using the first man on the moon I used the first man in space."
He added: "I wanted the film to be fun and surprising and to give hope."