Apollo: The Race to the Moon

Seconded, phenomenal book and suggestion. IMO in a similar vein is 'The Making of the Atomic Bomb', Richard Rhodes, another industry- and world-reshaping project.

Not totally what you are looking for, but I'd highlghly recommend "Apollo" by Murray and Cox. It focuses on the engineering history of the Apollo program, and it is a superbly well written and researched worked and so many of the stories are about engineering philosophy that I think it'll really be worth your while.