Depends on how committed you are, but Shelby Foote's The Civil War: A Narrative is pretty much the gold standard in Civil War history. It's a three volume work, very long and thorough.

If you haven't already, you might consider watching Ken Burns' Civil War documentary series. It is available on Netflix, if that's an option for you.

I think this might help you.

1861: The Civil War Awakening by Adam Goodheart: A popular history book that discusses the mood of the nation in the lead-up to the Civil War

Battle Cry of Freedom by James McPherson: Widely considered as the seminal one-volume work on the Civil War period, focusing holistically on the economic, social, political, and military aspects of the time.

http://www.reddit.com/r/AskHistorians/comments/timi4/the_askhistorians_master_book_list/

Why the South Lost the War by Richard E. Beringer is a good one. Gives a lot of insight as to several reasons why the South ended up losing. Pretty much anything by James McPherson is great as well.