What an absolutely wonderful + thoughtful idea OP! Sounds to me as if you would like everything to start off on the right foot and I am pretty sure it will considering that you are already so considerate of your new nanny's personal needs.
That being said, for her welcoming basket I would include: a Starbucks gift card, a Target or Walmart gift card, a bath set (body wash/lotion/body mist), a towel collection, a few current issues of a Women's magazine, razors and some Altoid breath mints.
