This isn't a book recommendatoin, but if you really want to get an in-depth understanding of the war, you might consider Professor Blight's Open Yale course.
Essientially, this is a set of 27 lectures (each lasts 40 - 50 mins), with the title
The Civil War and Reconstruction Era, 1845-1877. Prof. Blight delivered the lectures at Yale in 2008. There is an accompanying reading list.
I took the course last year, when I was stuck at home after a cycling accident. It's quite daunting, but you can do it at your own pace, and repeat anything that you didn't catch the first time. I only read a few of the items from the reading list, but, after each lecture, I reviewed the relevant material on Wikipedia to help re-inforce it.
The course is entirely free, and you don't need to register. You can access it at
http://oyc.yale.edu/history/hist-119.
I also read McPherson's
Battle Cry of Freedom , as well as the books by James Swanson mentioned above.
I wish I could get a copy of the Burns TV series, but it doesn't seem to be available over here.
Mike