OK, this is verbatim (and extemporaneous) from our resident Beatles fanatic. He's been reliable (when it comes to anything Beatles) in the past, but I can't personally vouch for it. He did recite this off the top of his head, though:
Real story, before Capital Recods in the U.S. picked up "I Wanna Hold Your Hand," a small record label called Vee-Jay Records released the following three songs "Love Me Do," "She Loves You, Yea, Yea, Yea," and "Please Please Me." However, due to radio stations' aversion at the time to any non-American rock and roll, they were not played on the radio. It was not until "I Wana Hold You Hand" that the major record companies and radio stations realized they could not ignore the music any longer and unleashed "I Wanna Hold Your Hand" upon the public. Thus, while the first "official release" was "I Wanna Hold Your Hand," due to the lack of airplay or attention given to the songs released by Vee-Jay Records, it is difficult to say which of them, if any, was the first.
He also claims that, while "I Saw Her Standing There" was indeed the first track on the first album released in the US, it was not the first single. The kid seems pretty sure of himself, but I encourage anyone to prove him wrong.