I am still struck by how bold this speech at Rice University was at the time. NASA had a total of two manned orbital flights under its belt – John Glenn in February and Scott Carpenter in May of 1962.
Those who came before us made certain that this country rode the first waves of the industrial revolutions, the first waves of modern invention, and the first wave of nuclear power, and this generation does not intend to founder in the backwash of the coming age of space. We mean to be a part of it–we mean to lead it. For the eyes of the world now look into space, to the moon and to the planets beyond, and we have vowed that we shall not see it governed by a hostile flag of conquest, but by a banner of freedom and peace.
8:40 for the moon challenge. At 10:20 he mentions building the Vehicle Assembly Building. At 10:55 he mentions the Mariner mission to Venus.