The bulk of the post-Civil War military action was on the Western frontier [1866-1898]. Check the usual sites for records on the cavalry, infantry and artillery units that waged war against the tribes west of the Mississippi River and Texas: Ancestry.com, Fold3, NARA and sites specific to battles.
The 19th century went out with the Spanish-American War , best known for Teddy Roosevelt's Rough Riders. The 20th century dawned with the War in the Philippines . Once again, check sites with military records and sites that focus on the engagements. ["Rough Riders"]