These are first rate books, but I generally recommend Shelby Foote's trilogy to a newcomer simply because -- in addition to being beautifully written -- it covers the war outside Virginia.
Foote is reputed to be a bit of a pill personally but he's an engaging speaker. He once teased a Virginia audience (in Lexington, IIRC) with the assertion that Virginians know less about the war than anyone else. This had the intended effect, which was exactly what you would expect in Lexington.
Once the smoke cleared, his humble point was that the Virginia Mafia is so preoccupied with Bobby Lee's defense of northern Virginia that they lose sight of whole chunks of the Confederacy being swallowed each year in the west. True, of course; the war was decided in the west.