I have recently spoken with a local rabbi, who happened to be sent from Chabad-Lubavitch, and he told me that one of the requirements of my life post-conversion would be to marry and have children. If one converted to Orthodox Judaism, would he or she actually have to marry and have children? If so, is this a requirement across all branches of Orthodoxy (Haredi, Hasidic and Modern Orthodox), or only certain branches?
This answer is intended to paint the basic obligations in very broad strokes. The details are beyond the scope of this discussion, and always ask your rabbi for more details as they would apply in your particular scenario. (Full disclosure: I'm not even close to marriageable age, so all of this is from what I've learned, not from what I've practiced.)
Just after creating Adam and Eve, G-d tells Adam to "be fruitful and multiply" (Genesis 1:28). Our Sages interpret this as a positive commandment to bear children (Maimonides, Ishus 15:1). Now, in order to bear children one must first get married, which Maimonides classifies as a commandment (Ibid. 1:1) based on Deuteronomy 24:1: "When a man will take a wife and marry her..."
Technically speaking, only a man is obligated in procreation (Ibid. 15:2), and he has not fulfilled his obligation until he has one son and one daughter, both of whom are capable of bearing children themselves (Ibid. 15:4).
The reason for these commandments are so that the world will not remain empty (Gittin 41b). To quote the verse in Isaiah (45:18), "He did not create [the world] for waste; He formed it to be settled."
It's noteworthy that this instruction to bear children is the first thing G-d ever says to Adam, and that His next communication with him is regarding a mate (Genesis 2:18 - see in particular v. 24 there).