I don't speak from a broad experience of reading many of these books, but I quite liked Campaigning with Grant by Horace Porter (1898).
Porter was a senior aide-de-camp to Grant in the last year of the war and was an unabashed admirer. It may be too Union-centric for you, but I found it intelligent and illuminating.
I lost my copy a couple of years back, so I can't provide any detail right now. Wiki's bio offers the essentials:
The Young Volunteer by Joseph E. Crowell is pretty good. He served as an enlisted man in the 13th New Jersey Infantry in the AoP. He doesn't see constant action but he describes the everyday life of the average Union soldier from his eye view, without getting too much into the grand strategical outlook on things. His writing style is very readable and he mixes in a lot of good and often humorous personal stories to boot.