Student or Learner
When they had returned from Venice, Rose had been unsure what she was supposed to be. While they were away, she had very definitely been a young lady – she had danced at a palace ball, for a start.
Can we say "for example" instead of "for a start"?
Not a teacher
I personally would not change "for a start", since it reffers to a list of other factors that could be added. You could say "for example" but it'd be in detriment of the writing style.