There is only one type of Schengen visa for short trips: the uniform short-stay visa known as "type C".
Apply for that from the Swiss representation, and describe the trip you plan honestly and accurately. There are checkboxes for "tourism", "business", etc on the application form, but there are not really any different rules about them -- the checkboxes just allow the bureaucracy to sort the applications into broadly similar groups where the same general kind of supporting documentation can usually be expected. You're free to clarify exactly what the purpose of your visit is in an enclosed explanation, and if you do so you won't be denied simply for having guessed "wrong" about the ordinary-case checkboxes.
That being said, it sounds to me like "business" would be a pretty good fit in your case.