But what kinds of knowledge should you import into your poor, overworked brain in order to produce the right output? It's not as simple as "learn halacha." I would argue there are many kinds of knowledge you need to acquire in order to integrate into orthodox society with the most success and the least suffering or embarrassment. There may be others, but these are the categories of knowledge that occurred to me.
Halachic knowledge: Ok, that's a given. However, pay careful attention to learning what is halacha, what is chumrah, and what is minhag. Those distinctions are important and often overlooked by the popular literature (and most teachers/mentors).
Hashkafic knowledge: Your hashkafah is your "worldview." It generally refers to your "brand" of halacha and Jewish living. At the broadest level, it is the label you wear: "just plain orthodox," modern orthodox liberal, yeshivish, chassidishe, etc. But hashkafah has implications right down to whether you are comfortable owning a TV or going to a movie theatre. (Explanation: if you go to a movie theatre, you might have to touch someone of the other gender's arm on the armrest, and that leads to mixed dancing.) Expanding your hashkafic knowledge means learning about your group's philosophy and methods of interaction with the world. In many ways this is minhag, but it's deeper than that. There's a rationale behind the action that's more philosophical than "this is what our community has been doing for 300 years." Tznius, women's issues, and interaction with the "secular" world are usually big issues here.
Historical knowledge: You're joining a people as well as a religion. The Jews have a unique history, and even the earliest history can still have ramifications today on the Jewish worldview. You need to be conversant with the gist of many periods of history. I would suggest the following level of "importance" as a guideline for your study, though your mileage may vary: Torah history, the exiles, WWII, the creation of the state of Israel, history of the great Sages (and/or their works), Tanach history, Israeli history (basically the wars), the periods of oppression in Europe from the middle ages until the Enlightenment, and then the earlier periods. I admit I know little to nothing about Sephardi history other than what is shared with the Ashkenazim (Blame American Askenazi privilege). I say "importance" based on how often these topics or themes come up in everyday life (conversations and shiurim), in my experience.
Cultural knowledge: From the borsht belt to Seinfeld to Yiddishisms (wow is that Ashkenazi-centric), cultural knowledge is just fun. It's also the best way to fit in: to get the jokes and to make them. It's knowing the slang, the values, and the buttons people push (for example: Rabbi Avi Weiss, "mixed dancing," the Maccabeats, Chabad, or anything else that can start a passionate debate). This is like a deeper version of historical knowledge. If historical knowledge is about joining a people, cultural knowledge is about joining a family. You will learn how your community thinks, what they are passionate about, what makes them angry, what makes them laugh.
Social intelligence: You need to learn how to get along with other people. People who may drive you insane sometimes. If you're going to get through the conversion process relatively unscathed emotionally, you need to understand group dynamics and how those dynamics can affect your life. You need to be able to think of far-reaching implications for your actions (and have the discretion to realize when those consequences are irrelevant). Social intelligence can be learned, but some people have more natural skillz in this area. Important: beware of confusing social intelligence with manipulation. They are very different, and I don't recommend mixing the two.
Knowledge of personalities: This is a subset of social intelligence, but even if you can't manage full social intelligence (or make a wrong prediction), you can at least work on your knowledge of personalities. As I have said many times, rabbis are people too. No person is entirely consistent or predictable. There are always facts beyond your knowledge. A rude rabbi may have nothing to do with you; any number of things could put him into a bad mood at the precise time you were scheduled to have a meeting. That doesn't justify rude (or unacceptable) behavior, but being able to judge people favorably will allow the bad experiences to roll off your back like water rather than rotting in your chest. Likewise, even if you aren't able to predict future problems through social intelligence, knowledge of personalities can help you analyze a situation after-the-fact to choose a new course of action. So maybe social intelligence and personality knowledge are two sides of the same coin?
Do you have any kinds of knowledge to add to this list?