AA is the best.
but if u want to fly BA transtlantic, QF is worth considering.
i would strongly recommend against BAEC(Asia)
if you want, use the european or UK address (or USA address), but my experience with BA Asia is 1.5 years ago.
the people in BA forum seems to disagree with me, but i havent got any expalnation though. see the recent posts there, and ask them why they disagree with me.
so based on what i know.
you might want to consider QF, then BAEC USA