Who decides what animal etc a Buddhist will be reborn as?

There is no "who" (god or gods) deciding anything in Buddhism. Your own actions direct your path towards enlightenment:

As far as your condition at rebirth there appear to be three factors at work:

  • Your life quality (how god a person you were in this life)
  • Your last thoughts
  • A wild card

The last is hardest to explain - apparently good people periodically and randomly (to our understanding) get reborn to a worse, not better condition.