As a fellow reenactor, I have to agree with Banjer. Brass bands may have been popular, but the soldier spent much of his time making music on anything he could get his hands on. Fiddles and banjos are the stringed instruments most often noted in diaries, letters and accounts. Remember, banjos were 4 string, fretless, and strung with cat gut. It didn't give the big bright banjo sound we hear today. Music in camp back then did not resemble the high quality studio type to which our 20th century ears are accustomed. Many a soldier boy noted that the musicians were perfectly awful. However, they likewise noted that the music was wonderful. The quality didn't matter. It was the comraderie and the joyous link to hearth and home that this music made for them that they treasured; hence, the banning of "Lorena" (as noted in a prior post) and other tunes that made the lads homesick. For books, I would recommend "Singing Soldiers" as noted above. It has been reprinted within the last few years and is now available in bookstores again. In addition to the fine recorded music already mentioned in other posts, I would add the recordings of Jim Taylor - several tapes of instrumental guitar, fiddle, hammered dulcimer - but especially his two vocal tapes. I don't know why he doesn't record more vocal music. Also, the 2d South Carolina String Band. Their tapes have more of a "sittin' round the campfire feel to them. You can also check out the 7th La. String Band, Hardtack and Harmony and a very nice new work called "The Irish Volunteer" by David Kincaid. Kincaid gives us a number of period tunes that have not previously been recorded by anyone and the presentation is great. I also highly recommend the Para, Barton and Dyer works and the 97th Regimental String Band. There is a Civil War music web site that has come a long way in the last year. I'm sorry that I don't have it handy but it comes up easily on a net search.
Your Obedient Servant,