Old history books about the Civil War are often full of historical inaccuracies and partisan misrepresentations as much as - if not more than - post-WWII accounts.
Shelby Foote's The Civil War and James McPherson's Battle Cry Of Freedom are two good post-WWII histories that get almost all the facts right and are very readable.
Foote's book is sympathetic to the Confederate viewpoint and McPherson's is sympathetic to the Union viewpoint.
Together they present a good layman's overview of the conflict, in my opinion.
1. Anything by Stephen Sears. Mr. Sears is the preeminent historian on the eastern theater of war during the civil war. His books are well researched and he is such a good writer that the narritive reads more like an adventure story rather than dry history.
2. Fighting for the confederacy by Edward Porter Alexander. Alexander was an arillery general for the south and participated in virtually every major battle in the eastern theater of war. His book is easily my favorite by a civil war participant. Not only does the book contain brilliant insights by this talented soldier, Alexander focuses very much on day to day events and anecdotes rather than what regiment did what in the various battles. Thus, you get a very good idea of what the war was like for the participants from the lowly foot soldier to the major generals. A great read.