You can get both CSA and USA service information off the Civil War Soldiers and Sailors System website. The VA does consider this source a valid one.
Also, The American Civil War Datbase (Civil War Data Systems), which is a for pay website, also has such information, which often included enlistment and discharge dates, promotions, etc.
If you have any other sources (censuses, obits, etc.) photocopies can be included with the tombstone request forms to further validate the man's service, unit, cemetery of burial, etc.
Hope this helps.
Also, I subscribe to the for pay site. If you need a record checked, let me know and I'd be glad to check for you.
Graves Registration Officer
Dept. of Oklahoma
Sons of Union Veterans of the Civil War