Don't forget some of the popular Minstrel and "Civilian" tunes of the period, like "Wait for the Wagon", "Lorena", "Poor Nellie Gray", and the Steven FOSTER hits like "Old Kentucky Home, "The Glendy Burke", and "Hard Times" (Parodied in the Army as "Hardtack Come again No More"). A favorite on both sides was "Home Sweet Home".
If you have the vocal range for it and want to impress the shucks out of yer Pards (provided that you can pull it off) try "Kathleen Mavourneen" By F. Nicholls CROUCH who fought in a Georgia Militia Artillery Unit throughout the War. It may be heard on the "More Songs and Tunes From Gettysburg" soundtrack recording. Don't know if it is on CD or not; I wore my cassette of it out.
One of my critisizims of the BURNS CW Series soundtrack is that despite his fairly competent renderings of such songs as he did, he neglected scads of really beautiful and compelling music of the period and repeated the same 5 or 6 tunes over and over and over...
It has been said that there was more music written in America during the ACW than at any other period in our history... and I am inclined to believe it. As I collect 19th Century music, more and more of it keeps turning up and God knows how much never got written down and was lost forever. One could easily devote a lifetime to the study of the Music of the American "Civil" War.