Though it is not a civil war game. I would look at the yet to be released
Empire: Total War. It will be an immersive strategy game were you can have large battles with intricate unit formations as well as a larger nationwide campaign. It will use period style musket weaponry.
I have played other Total War games and each is unmatched in terms of scale of battle, importance of formations and unit balance. Not only does the sheer strength of units matter but if units take heavy casualties, get surrounded or take sudden swift losses though minor they will panic and flee the battlefield causing your lines to panic and bolt too.
In the campaigns you run a whole empire managing the economy, politics, population growth and the happiness of the communities.
These games also have had a heavy modder community so I am sure people will make custom civil war units possibly maps.
Unfortunately it is not due to be released until February 2009. Though in the meantime I would try out Rome: Total War and Medievel II: Total War.
Here are a bunch of
Civil War games on Amazon.
The history channel has made several Civil War games. A recent one is simply
History Channel: Civil War. It is a first person shooter though.