A list of the arguments the Socrates’s uses in his defense should probably include his point about how he’s telling the truth. According to Socrates, he’s not corrupting the youth; he’s pointing out what they already know: a lot of people, especially those with power, claim to be smarter than they are. The youth, according to Socrates, “take pleasure in hearing people questioned.” He is not leading them astray. He is doing something that they were already inclined to do.
Another argument to list involves the suspicious character of his accusers. Socrates tries to sow doubt about the legitimacy of the accusations. According to Socrates, rather than admit that they have “proved to lay claim to knowledge when they know nothing,” they have orchestrated these phony charges against him. Socrates defends himself by painting his accusers as slanderous and malicious. He’s on trial to cover up the fact that his accusers can’t stand that he’s exposed their faults.
As for the charge of not believing in the gods, Socrates defends himself by pointing out the paradox of the accusation. If Socrates believes in “spiritual things,” then he “must quite inevitably believe in spirits.”
As for the list that would persuade someone of Socrates's innocence/guilt, that will depend on the juror in question. A juror who is suspicious of power might find his argument about the mendacious character of authority persuasive. Conversely, a juror less questionable of authority might find Socrates’s argument disrespectful and thus will be more inclined to find him guilty.