1. Check the 1930 United States census. A question in that census asked if anyone in the household was “a veteran of the US military or naval forces mobilized for any war or expedition." The war or expedition was also specified. The 1930 census can be accessed for free through a cooperative between FamilySearch and Ancestry HERE.
2. Another way to identify ancestors involved in The Great War is to simply look at dates. The first and second drafts called males born between 1886 and 1897, and those drafts occurred in June 1917. The draft of September 1918 spread to a much greater age range.
After your initial fact finding is finished, you may want to try searching in some of the resources I will share beginning next week.