If you truly want to experience the history as it happened. There are many archives on line where you can read Civil war vintage news articles. What is especially interesting is reading about a battle or campaign and reading it as printed in a Rebel newpaper and then reading the same thing printed in a Yankee newspaper. It's amazing how different they are. It's also eye opening to read today's revisionist (PC) version. A good source (for those interested) is Civilweek.com. The site has excellent resources but appears not to have been updated in several years. If you want a particular week in the war you have to walk back from the last page to the first.
It's interesting how historians clearly see how the media was biased in the past and yet modern journalists claim they are completely objective.
The winners write the history; the loosers cry, "foul".