From what i have seen the candidates are chosen by the holy grail itself. Usually a person who is a master or whose family are or were magicians.
Also yeah lancer's master is pretty slick, If all this was planned by him, which i suspect it was.
------------------------ Possible spoiler ( my theories)---------------------
I had always wonder why the mediator was in the first opening, explaining the holy war. I knew he had a great purpose. Why was it him instead a more proment character?
I think it was planned because in the last war, the holy grail was destroyed, by saber's master, shirou's father. He did not win the war but the grail appeared to him anyways. He had saber destroy it. I think that he feared gilgamesh getting his hands on it. This brings up another question, who was gilgamesh's master. Who took place in the last war and is in this one now, is there a connection? I believe so.