Short answer: e/em/eir, look up "Spivak pronouns" if you're interested in their history.
Long answer: I wish it didn't matter, and that any that seem respectful to you would be fine. When I know they're being respectful, people are welcome to call me "he" or "she" depending on context. Where those pronouns are the only options, I'm a she as that matches my gender as registered with the state.
The trouble with pronouns is that they get used to express disrespect. For example a man may get called "she", a woman may get called "he", and both may get called "it". When you make clear you don't believe someone is a "real" woman or man, you're not just overstepping a boundary: because we live in a culture where every human being is assumed to be a man or a woman and nothing else, you're implying they're not a real person. This is already disrespectful to people who are not trans, but it is even more dehumanizing to those who are. Many of us have to go through a process of proving we're "real" before we can get access to medical treatment, in which we have to live through the humiliating situations that the same treatment helps prevent. Trans people do not get to be the ultimate authority on their own gender like most people who aren't trans do.
You may have been taught that if you disagree with someone's pronouns, you can call them "they" as a compromise. Don't do this, it's passive-aggressive behavior. If you can't speak about a person without showing that you think you understand them better than they understand themselves, it's better not to speak about them at all. They/them is for groups, for individuals whose pronouns are completely unknown, and of course for people who tell you that those are their pronouns. Similarly, don't call anyone "it" unless they ask you to.
So why do I like being referred to by pronouns that were invented to avoid implying a person is a man or a woman? Isn't this self-dehumanization? One reason I like this is that it will confuse the people who think of trans men as "women who want to be treated as men", and trans women as "men who want to be treated as women". If people can't play nice with the knowledge of what my assigned gender was, then I refuse to give them that toy.
Another reason is rooted in the way trans people who seek medical treatment have to prove they're "real". We have to match someone else's stereotypical ideas of what it means to act and dress like a woman or man in order to get access. People around us also push us to match stereotypes, while at the same time others consider stereotypical looks and behavior to be "proof" that we are not "real". If I weren't trans, I could be myself and be accepted as a man or a woman (yes, I really could fit in either role), but because I happen to have this upsetting problem with my body, the rules are both more strict and intentionally impossible for me. This is some top grade bullshit that I won't play along with.
So e/em it is. Or, if I gave you permission, she/her, or he/him, or even they/them, or some fancy neopronouns, those can be fun. I feel most free around people who know how to make mixing pronouns sound right. One more thing: please don't correct others unless you can tell they're trying to be mean!