Gendry, he is the only son (bastard) of Robert Baratheon alive. We don't know where he is but he seems to be the only legislative claim of Baratheon descent. That was the only fear of Joffery which made him kill all the bastards to eliminate any such claim.
Other claims are just going to raise opinions, like Starks deserve it because they were also responsible for winning the war against the Mad King, or the Targaryens because they ruled before, etc etc.
Note: As per the books things are different as there is one more Targaryen claim and Stannis is still alive with his daughter. So as per the books Stannis' claim is more legislative as bastards don't stand against true blood.