I think Love Me Do is a more logical choice for a first song. I think it is better than anything else they had at the time. Remember, that most of the other A&R men around in England rejected them. George Martin was a risk taker. He was the only one around that recognized their talent. I think he was a little skeptical as well. EMI as a whole had rejected them. Parlophone was a label for mostly comedy records, and off beat recordings.
At the time, as funny as it sounds now, they were only partially ready for the big time. I personally don't believe it, but it has been speculated that Brian Epstein bought most of the copies of Love Me Do/PS I Love You so as to make it chart. I know this does not answer which song should have been used as the A-side, but the point I am trying to make is this is the best they had to offer at the time. Please Please Me was not written or completely worked out. As I said above, Love Me Do is the more logical choice.
