Some of my favorite memoirs are
Company Aytch by Sam Watkins
Hardtack and Coffee by Josh Billings
Fighting for the Confederacy by E.P. Alexander
Campaigning with Grant by Horace Porter
If you have the chance to visit some battlefields, try and read the Army War College Guides first (published for Antietam, Chancellorsville, Gettysburg and maybe others....)
Another good memoir is All For The Union: The Civil War Diary and Letters of Elisha Hunt Rhodes. A good small scale view of a typical unit of the times would be Mother, May You Never See The Sights I Have Seen: The 57th Massachusetts Veteran Volunteers in the Last Year of the Civil War, by Warren Wilkinson.