I thought I may be of some help in terms of history books given that I’m studying to be a historian and read many history books. Unfortunately there aren’t many historians who do much integrating in terms of tying events together very well. But many do a good job in at least telling particulars in a way that is interesting and thought provoking.
If you want ancient history of Greeks and Romans I would recommend the ancient historians Xenophon, Livy, Thucydides, Procopius, Appian, Tacitus, et al. They are all crucial in any understanding of what happened in those nearly forgotten days, and it is from them mainly that all historical work about that period sprouts from. Josephus is also good, though somewhat biased. For a great work detailing the end then one should look no farther than Edward Gibbon’s Decline and Fall of the Roman Empire, a work that does attempt to integrate and make sense of the end of the Rome and generally succeeds, plus modern historians hate it, which is always a good sign.
For medieval history look to William Manchester’s A World Lit Only By Fire. Most other books on the subject are too lamenting of how things weren’t so bad during the time period or else focus on the irrelevent, like what were women doing in the middle ages, or what songs did children sing in the middle ages.
American history is a mixed bag. Older history, like the works of Washington Irving, his Life of Columbus and Life of Washington are good. Paul Johnson has done good work in the field, as have particular biographers of various founders. Flexner’s biography of Washington is good. Bradley’s biography of Adams in excellent. I’ve never really read a book on Jefferson that I particularly liked. Ketchum’s book on Madison is also good. A wonderful book about the French-Indian War and its effect on the revolution called Crucible of War is a fantastic read, it’s by Fred Anderson. Unger’s biographies on Lafayette and Hancock are interesting and Brookhiser is readable. Henry Adams is a rather poor, and hence overrated, historian whom I would avoid if possible.
Military History is usually better than other kinds of history. JFC Fuller wrote many fine books as did BH Liddell Hart on a wide variety of topics. Southey’s Life of Nelson is excellent. Churchill’s histories are very interesting, My Life is good as are The History of English Speaking Peoples and the The World Crisis. Ross Leckie also wrote many good military history books, all about American military history.
For Russian history Richard Pipes is excellent. Shirer’s Rise and Fall of the Third Reich is very good, and used quite a bit in Peikoff’s The Ominous Parellels. John Keegan is probably the best military historian still alive, he has written many interesting books, including The Mask of Command and The First World War.
For illuminating books on the lies surrounding communism in America and the coverups perpetrated by liberal apologists during the cold war go to John Earl Haynes and Harvey Klehr.
Finally I cannot stress the overall importance of the writings of the men who were there. TE Lawrence, James J Hill, Fuller, Churchill, Eddie Rickenbacker, Caesar, EP Alexander, Patton, Chuck Yeager. All these people have written excellent histories.
Betsy mentioned fiction telling a great deal about history, this is certainly true. Dumas, Hugo, Walter Scott, Defoe, Dostoevsky, Tolstoy, Dickens, Jack Higgins, Ed Cline, and CS Forrester, just to name a few, all used historical events and persons very effectively in the telling of great stories.