Start with his father’s, Michael Shaara’s, The Killer Angels, a novel on the battle of Gettysburg…
The best one volume book on the Civil War is James M. McPherson’s Battle Cry of Freedom.
From there you can go onto Shelby Foote’s trilogy on the war, now available in a one volume edition. Be warned: it is immense. He spends up to 250 pages on single battles.
For a shorter, more traditional and northern perspective, there is Bruce Catton’s older Civil War trilogy: Terrible Swift Sword, The Coming Fury, and Never Call Retreat. He also wrote The American Heritage New History of the Civil War (updated by McPherson), excellent like all the American Heritage books are.
Geoffrey Ward’s illustrated history, The Civil War, accompanies the Ken Burns documentary, which is available at libraries everywhere and is one of the few works of his I think really works.
The war lead to Reconstruction and you can go there with Eric Foner’s book of that name.
Robert William Fogel & Stanley L. Engerman’s Time on the Cross is a controversial but fascinating look at slavery.
On a lighter note, Margaret Leech’s Reveille in Washington is a marvelous look at the city during the war, with much commentary on Lincoln and others. Gore Vidal’s Lincoln: A Novel is his usual astringent look at the city of that same period.
There are a million biographies of Lincoln. I happen to have Benjamin J. Thomas Abraham Lincoln. It’s a good place to start.
For the southern equivalent, start with Roy Blount’s brand new Robert E. Lee, an entry in the excellent Penguin Lives series of mini-biographies. Douglas Southall Freeman is the grand old man of the southern viewpoint, perhaps a little too southern for today’s tastes. Still, his books can’t be beat, if only for length. Fortunately, there is now a one-volume abridged edition of Lee available and you can go on to his war study Lee’s Lieutenants also now available abridged (at 912 pages) if you really want to get into it.
I don’t have a recommendation for a bio of Jefferson Davis. I read some ponderous tome many years ago and had enough. But there have been a number of new biographies in recent years for you to try, including several that compare him and Lincoln.
Ken Burns and everybody else quotes heavily from the diaries of Mary Chesnut for how it felt to live in the South during the war. A Diary from Dixie is the thing itself (abridged) but C. Vann Woodward’s Mary Chesnut’s Civil War gives more background and annotation.
It used to be said you weren’t a Civil War expert until you had read 500 books on the subject. Today you probably need to read 1000, just because that many more have been written since that comment was made. I haven’t touched on any of the specialized aspects of the war or individual titles on the battles because there are just too many.
But these ought to keep you out of mischief for a while.