I'd probably start with Battle Cry Freedom by James McPherson.

It covers the whole war. It's really well written so it carries you along and is as enjoyable as such a topic can be. It covers the major events without being overwhelming and is a good book for getting a big picture view of the different campaigns. There are about a million copies floating around so finding it at the library or used won't be difficult. And even though it's somewhat dated, it was much better about avoiding Lost Cause stuff than Foote.