You definitely want Battle Cry of Freedom. It's got all the classic military history stuff with maps and battles that McPherson talks you through as well as a large helping of the non-military aspects of the war. As a bonus, the chapters on the antebellum are an excellent first introduction to the subject.

While I do not know "Delivered From Evil", when you are looking for a single volume history of the Civil War then McPherson's "Battlecry of Freedom" is a good choice. It's very well written, covers the pre-war-time, all theaters, all war-years, foreign aspects and the "homefront".

I second the recommendation of Battle Cry of Freedom.