In your opinion, what should A do when it comes to Nathan? Explain why you think this is A’s best option for handling the situation.

This is definitely an interesting question! It will be hard for us to say what A should do, since we are not A. A's choices are often based on life experiences. While the novel gives us a glimpse, we don't have the experiences that A has. We don't know what's it's like to be in that situation of always switching bodies.
First of all, we can say A never should have gotten into that situation. Even if A wanted to go to the party, A should have made sure to set an alarm to ensure Nathan was home in bed before midnight. A should have double checked to log out of the email and clear browsing history.
I think my first instinct would be to ignore the emails from Nathan. I would try to pretend no one checks that email address, or maybe even respond pretending to be someone else: "Sorry man, I don't know what you're talking about!" However, that wouldn't really solve any problems, since Nathan would still go to the police and media, telling his story and asking others to come forward.
Let's explore what options A has and think about potential consequences. A could respond right away and try to explain before Nathan tells his story, but perhaps Nathan would show that email to others—though no one believes Nathan, so maybe it wouldn't matter if he showed A's emails. People might think Nathan faked them.
A could fabricate a story, such as telling Nathan that he was possessed by an angel doing the Lord's work and that Nathan should just accept being part of God's plan. Perhaps Nathan would believe this, since Nathan seems religious to a certain extent; he turns to a pastor for help and calls A the Devil. However, just as Nathan says "prove it" when A claims to not be the devil, Nathan may require proof of A being an angel. Nathan might also believe it, but then still request that A come meet Reverend Poole.
My first instinct is to say that A should not meet Poole, given the danger that puts A in. However, it was also important for A to have this meeting and realize there are others out there.
In the end, I think A's choice to try to ignore the messages, then dispute them, and then meet with Nathan end up working out. Even if they seem like mistakes, I think they are important in forming A's character.