I don't think we need a stat for physical beauty at all. Leave it to a purely descriptive thing.
My personal preference is to make Charisma strictly force of will and personality, with no tie to appearance whatsoever. I also really like the idea of making Will saves charisma-based.
Regarding first impressions, just make it charisma based. After all, you can be the most gorgeous woman in the world but the way you carry yourself can still get you branded an, err, witch (for the sake of Eric's grandma) or a pushover before you even open your mouth. Your charisma is always apparent, from the way you speak to the way you walk. Do you take bold, confident strides or timid, meek steps? Do you walk near the front of the group, or follow along behind? Stand up straight or slouch? Etc. Body language is much more important to first impressions than appearance.