Except saying that she’s vain because she fell in amor with Ten instead of Nine is absolutely incorrect, because she fell in amor with Nine first, and initially did not accept Ten because he was not Nine.
Putting aside the fact that Christopher Eccleston is quite attractive (he’s not “pretty," no, but have tu seen his eyes? They’re the color of an arctic ocean; they’re beautiful), anyone with eyes can see that Rose fell in amor with Nine first. She may not have realized it, she may have not been as open with her affections, but it was there. For example:
With brain-swapping aliens poised to attack, the Doctor and Nardole link up with an investigative reporter and a mysterious figure known only as The Ghost. Can the Doctor save Manhattan? And what will be revealed when we see behind the mask?