If you want to play right out of the box then Avalon Hill's "Battle Cry" is good. For an overall Civil War game look at "The American Civil War" by Eagle Games.
If you want to buy and paint some miniatures I suggest you pick up the rules for Johnny Reb
If you want to play large battles such as Gettysburg etc, Fire and Fury is an excellent set of rules. They have good illustrations of how the rules work and are not overly complicated. Fun to play too!