In your opinion, what are some of the best books/papers on Newton and his work that accurately cover the connections between his geometric proofs in the Principia and his development of the calculus and his disputes with others on these topics?
So far, some articles in The Cambridge Companion to Newton seem pretty good to me in addressing the interplay between Newton's calculus and his geometric proofs of physics in the Principia as well as the associated disputes on priority and philosophical approach (physical intuition versus pure algebraic manipulation). See also the intro of Needham's Visual Complex Analysis.
Edit March 2020: This question is about Newton's mathematics, but I can't resist quoting Keynes on Newton, which aptly places Newton's diverse interests into an understandable perspective:
Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind that looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago.