Literally tens of thousands of books have been written about the war, its precursors and its aftermath. I second ahtollef that Battle Cry of Freedom the best general overview of the war, but are you interested in anything more specific about it? (Military, political, international, women, African Americans, economic, cultural, pre-war, Reconstruction and aftermath, Border States, Lincoln, the home front, and so on)

P.S. There probably isn't a "true" story about the war, or most anything else in history.

Battle Cry of freedom by James M McPherson or any Eric Foner books.

For the southern home front and how the war swept away the old south, I like the Fall of the House of Dixie by Levin.

But for an intro, everyone else is right, MacPherson is the way to go.

Hands down : Shelby Foote's trilogy The Civil War: A Narrative, as recommended by /u/coinsinmyrocket.

Bruce Catton's trilogy published in the early to mid-1960s as part of the centennial remembrance of the War, was my starting point. The trilogy is comprised of The Coming Fury, which gives a lead-up to the Civil War and ends with the first battle of Bull Run; Terrible Swift Sword, which recounts the formations of the two opposing armies into professionals (as well as the expediencies the opposing governments, their officers corps, and their common soldiers took in a conflict that grew increasingly out of control in terms of bloodletting; and Never Call Retreat, the volume that gives a very good overview of how the war was brought to its conclusion in every step of the way.

There are newer histories and many of those surely offer more modern scholarly viewpoints, but Catton's is a generally fair and really informative account on so many issues surrounding the convulsion that led to the founding of the current--arguable--republic here in America. I also said it was fair, and I meant that the books' treatment of each side's notable figures and events is unbiased, given their publication dates.