I would suggest providing him with other toys that he can chew on also one of those ropes that he can play tug with you. If he starts to bite you while u and playing with him then get up and walk away he will quickly learn that if he is aggressive during playtime then playtime is over.
I would choose the breed that suites your lifestyle best and then train for agility. Any dog can do agility, but remember the dog will be a pet first, so be sure you understand what you are getting yourself into first.