Joseph P. Kennedy III is the first of his generation, a tribe of dozens of cousins many of whom do not bear the Kennedy name, to make a bid for public office. If he is successful, he could renew the luster of a somewhat tarnished family name. If he is not, he will fuel critics’ claims that the family has exhausted its political potency. His road into politics has taken him from prestigious colleges to the Peace Corps to a job as a prosecutor.