I come down on the just call me an American side. It is important, more important, to me anyway than the rest. If you want to tell people about your ethnic or genetic origins that's fine, I always appreciate hearing about it. But that's a different subject.
Of course the problem with saying we are Americans ignores all non-US citizens who are from the Western Hemisphere. Canadians, Argentines, Cubans and the like are also American. No real solution here, we are a country without a unique name, except perhaps United States of America.
Right! And we should not be. According to my DNA test I could call myself a Neanderthal-American, 3% anyway.
When and where I grew up that was the most respectful word to describe people like you. Fortunately my parents made sure it was the word I used. Many of my friends used less respectful words. Now however I have trouble sometimes using other things like African or Black. Colored still seems respectful to me, but I know it doesn't to a lot of others. It is still the word long engrained in my brain.
Rob, the older, but still kicking American.