Hi Laini,
Erato is correct in saying that American is not an ethnicity, although Native American is often lumped in with East Asian ethnicity by the major DNA testing companies eg 23andMe. Modern Americans have their roots in Europe, Africa and Asia etc.
You were asking what DNA test might be useful in searching for a possible recent American "GI" ancestor. Well the best option would be an Autosomal DNA, which would give you ethnicity/admixture estimate and cousin matches. If your grandfather was from the USA then you may find cousin matches or even close family in the States.
I would recommend that you contact a group called
GITrace http://gitrace.org/index.html This group was set up to help people find their GI fathers and family.
Don't ignore ethnicity estimates as they can be useful. I speak from experience! My Ancestry DNA showed 22% Asian, although my mother was German and my father was English. I tested with other companies and got up to 25% South Asian (Family Tree DNA) My updated ethnicity at Ancestry DNA shows 19% Southern Asia, 2% Western & Central Asia-Gujurat, and 1% Burusho-Pakistan. Further tests within the family proved that my biological father was actually an Anglo-Indian serviceman. I have been able to make contact with members of my biological family. Although my biological father has passed I have been welcomed as a member of a very global family.
At the GITrace site you will find Ute's Page (Ute Baur-Timmerbrink) which talks about Children of the Occupation-
Besatzungskinder. To quote;
"
Between 1945 and 1955 hundreds of thousands of children whose fathers were soldiers in the Allied occupying forces, were born in Germany and Austria.
Many of these so-called Children of the Occupation have never met their fathers from the USA, Great Britain, France or the former Soviet Union. Very often they experienced exclusion from society and even from their own families."
Even if nothing unusual shows up in your ethnicity or admixture estimate you may find useful cousin matches. Moreover, it is worth testing your mother as well as your self, if you are able, as the matches will appear closer. Ancestry DNA has the largest membership with over 10M DNA clients worldwide but with a huge USA database. Christmas sale prices apply.
Good Luck with your search!
pughcd