A good analysis of US foreign policy is "Abraham Lincoln Deals with Foreign affairs", also published under the title "Diplomat in Carpet Slippers" by Jay Monahan. This is a classic study originally published in the 1940's and it does a good job of describing the international situation that almost erupted into WWI. The Civil War is too frequently seen as purely a local, regional conflict, but in reality there were huge international implications.
Another critical analysis is a book entitled, "Freeing Slaves, Enslaving Free Men" by a historian/law professor whose name escapes me. It was a very good analysis of slavery, the war and other aspects of that era from something of a pro-southern point of view. Do a Google search and you can get the author's name, I think. I strongly recommend this book.
I personally enjoy reading letters and speeches of historical figures from this era. They were quite literate, they wrote wonderful prose, and they expressed themselves in the words and manner of their own choosing without the ghost writers, speech writers and handlers who dominate what passes for the public discourse today. The speeches and letters of Abraham Lincoln area available in a number of editions, all the way from single volume collections to the full, blown 8 volume Rutgers University edition of the Complete words of Lincoln (Eat your heart out. I got a set for $15.00 on EBAY). I'm slowly working my way tho rough it, although I have read most of the main speeches and writings of Lincoln over the years. His prose is magnificent.
I enjoyed "Sherman's Civil War" a collections of the civil war correspondence of Wm. T. Sherman, commencing with letters he wrote at the beginning of secession when he was head of the state military academy in louisana! Sherman, that great southern nemesis, actually spent a great deal of time in the pre-war south, had many friends there, and greatly admired and enjoyed many aspects of Southern culture. Sherman was a gun nut and a hunter. This book contains 900 pages of Sherman's personal and official correspondence, an amazingly prolific output by one of the war's most active and energetic generals in an era before the invention of the typewriter or computerized word processing. Sherman was a strategic thinker and a commander of great intellectual depth and considerable ability. Strongly recommended.
Sherman's memoirs are also strongly recommended.
I recently finished "The Rise and Fall of the Confederate Government" by Jefferson Davis and it was a wonderful read. Davis makes a well argued, well documented case for the "compact theory" of the Union, whereby individual states were free to dissolve the union and withdraw from it in much the same way as individual members of a partnership or a joint venture. I found it very informative, well written and well argued...even if a bit tedious at times. It's in two volumes but is worth the effort if you are willing to make it. It's well organized so that you can skip around if you don't want to plow through both vols. from cover to cover. I think it is a must read for any serious student of this most tragic and turbulent era of American History.