As basic texts, I am suggesting either of:
Both are lengthy, but as we go I can suggest some nuggets in each that should not be skipped over lightly. Both books are available in paperback. In each biography, you are reading of historical events but also of the character and personality of Harry Truman.
If you are looking for something less hefty than the Hanby or McCullough biographies, you might consider one of the following Harry S. Truman by Robert Dallek (Henry Holt & Co. 2008) or Citizen Soldier by Aida D. Donald (Basic Books 2012).
For comments by and about President Truman, Plain Speaking by Merle Miller (Tess Press 1974) is a gathering of comments by him on the numerous personalities with whom he had contact, about the events of his life and comments of others about him and what he had done. These offer special insights into Truman’s personality. Another book with numerous reflections by Truman on history and persons is Where the Buck Stops edited by his daughter Margaret Truman (Warner books 1989).