One requirement, frequently abused, is that the veteran does not already have a marker with inscriptions. I assume his "native stone," would not preclude obtaining a stone.
If he's buried in an active cemetery, you'll need Cemetery Management to sign the form noting they will accept receipt. Also, in many cases they will complete the paper work for you.
Upright monuments weight about 300# and are set 20" in the ground. You'll need a good working party to set. Local Sons of Confederate Veterans Camps will usually assist and provide a Memorial service.
George Martin
Burial and Memorial Benefits Home http://www.cem.va.gov/
See especially the last line: Pre-World War I Era Headstone and Markers
Note: Proof of military service prior to World War I requires detailed primary documentation, such as Compiled Military Service Records (CMSR), extracts from official State files, Federal pension documents or land warrants, to be considered for a Government-furnished headstone or marker.