You are def right. Doing good research must be my top priority, but I was a little worried about doing an excellent job without PI not physically being in the US.
Just a quick question about getting a green card, does it seem to be difficult to get a green card without PI not being in the States? Of course, it will mainly depend on my research accomplishments, but I am worried since I have to get reference letters from several people. Can people outside the States write letters and be effective?