Your set list is almost entirely what I would call "country".

"Wreck of Old 97" (ca. 1910) and "Wildwood Flower" (ca. 1859) were pop tunes that passed into old-time tradition, and could be old-time, country, or possibly even bluegrass depending on how they were played. And I consider John Prine to be modern folk or country-folk more than actually country, but that's a personal view.