I am applying to join a research group in a school in Switzerland and after the first round of interviews, I have been invited by the university in Zurich for an in-person interview so that I can meet the research group and give a presentation on the work I am currently doing. I intend to be in Switzerland for just a night and I am wondering what kind of visa I should be applying for? Should it be a business or tourist visa?
There are no "Business Visa" in Switzerland. There are only short-term (Type C) and long-term visa: in your case, you'll need a short term visa, the details can be read at the FAQ of the department of foreign affairs.
You will need to fill out a Schengen visa application and check "Study" in the "Main purpose" Box.