Conversion

Although ethnically I am partially Jewish and have been very involved in the Jewish community, it's not through a matrilineal line, so I am not halachically Jewish --- and I am getting ready for my first meeting with a local rabbi to begin the formal conversion process. This is something I have wanted to do for a long time. While I am of course saving my questions for him - I have one question about the initial meeting that I am hoping to find the answer to on my own: We will be meeting at his office in the synagogue building. When I go to services at a synagogue, I always wear a kippa while there. I, of course, do not wear one outside as I don't want to misrepresent myself. My question is: For this initial meeting, since it's in the synagogue building but not in the sanctuary itself... should I wear my kippa out of respect for the rabbi and the space? Or should I not wear it because it is just in his office and I am just in the formal conversion process? I don't want to do anything to inadvertently offend or seem inappropriate. For context, I am meeting with a Modern Orthodox Rabbi. Thank you in advance!

So, I am technically not Jewish, because of the matrilineal rule. So, by that rule, if I'm correct in my thinking, I'd have to convert. Unfortunately, my father, though Jewish, is not practicing, and therefore, I was not taught any information and I need to know that in order to live my life the way it should be lived. I am new to the idea of even being religious, as my mother is an atheist, and prejudiced against religious people. So, if I could have some assistance on how to start learning when I have no ability to go to a temple in person, that would be extremely helpful. Thank you!