Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
Welcome to FT!
Unless you're hoping to travel to France during the high-demand summer months, I'd suggest flying AA/BA between JFK and LHR, but crediting all of those flights to AA's frequent-flyer program (AAdvantage).
After a few months (and at least four flights on AA metal), you should have AAdvantage Gold status, and a few months after that, AAdvantage Platinum status.