There is a lot of these. For the basics of American spaceflight, Baker's
A History of Manned Spaceflight is hard to beat. (Conspiracy fans should
do a compare&contrast between Baker's Soviet history and what is know
today.)

How could you not include Chaiken's A Man on the Moon?

Kranz' book is good. His boss' (Flight, Chris Kraft) is better. Collin's
Carrying the Fire is better than either.

Haven't read any of them yet, but I'll have to sometime. I'm currently
reading a book called Tracking Apollo to the Moon, by Hamish Lindsay. It's
good, covering the programme from an Australian tracking station point of
view, although there a numerous typo's, wrong names, and that makes me
wonder if some of the other details are wrong too. Interesting book though,
and some good pictures. Thanks,

David