Call me crazy, but I think Papa would have been a good single. People started liking Vanessa because ATM was so catchy and everyone wanted to learn it on piano. Private Radio is a catchy song indeed, but other than the little solo she does in the bridge, the piano playing is not very noticeable. However, Papa is all about the piano, and people would have gone crazy when listening, and everyone would have tried to learn the song at home. Not only that, but the dark theme of the song would have got V a more expanded fanbase and would discover other dark-ish songs like HAWBTW and C'est la Vie.
That's what I feel about the second single thinking of the record label and V's place in the mainstream, being objective. But thinking about which song I like the most, I would've chosen Who's To Say or Afterglow.