We in St. Louis are fortunate, in that 20th century American military records are housed at the National Personnel Records Center in North St. Louis County.
As far as World War I service records are concerned, however, NPRC is actually not a good source for many persons seeking records of U.S. Army veterans, as 80% of those records burned in the terrible 1973 fire.
Records of Navy and Marine Corps vets were not affected by the fire.
People seeking info on Missouri Army veterans of WWI would be better served at Missouri Soldiers Database.
Persons seeking info on WWI casualties can consult three sources, one of which is the BIRLS file on Ancestry.com (accessible for free at Central Library and our branches).
The WWI draft records on Ancestry.com can also provide info on some WWI vets (men already in the armed forces did not have to register). Your search on Ancestry.com will likely also produce “Suggested Records” that can add additional information about your veteran’s life prior to and after his/her military service.
I teach a class on "Records of WWI"--in fact, just did so at Northwest Branch Library (High Ridge, MO) in mid-March. I can send you a copy of that handout if you email me here. I can also offer that class to your metro-area group (for free) if you email me at that same address.