I am travelling to France for 6 days for a conference. After that, I want to sightsee in Switzerland for 4 days. Do I apply for a Schengen visa for France or for Switzerland? Should I apply for the conference visa or tourist visa?
There are a few rules that might appear to contradict each other in some cases but this one is pretty straightforward. France is the main destination, both in terms of length of stay and motivation for the trip (a conference typically trumps sightseeing, that what makes you travel to the Schengen area at this particular time). It doesn't really matter legally but it's also the first country you will enter. You need to apply with the French consulate in your place of residence.
For completeness, note that there is no such thing as a conference visa or a tourist visa. What you get in all cases is a Schengen visa, which covers both of these purposes (and many more). Simply check both boxes on the application form.