All three countries are special:
1) Switzerland is more of the most scenic countries in the world. Also, it is one of the cleanest. However, it is about 50% more expensive than the surrounding countries of Germany, Austria, France and Italy. I recommend Interlakken as a great base. Lucerne is worth a visit. Lots to see in that country.
2) Italy is loaded with history (ancient, medieval, Renaissance and modern), also tons of art and scenic places as well. The big three of Rome, Florence and Venice deserve about 12-14 days alone. There are many other great places in Italy, but his is your first trip.
3) You immediately think of Paris, but we love Normandy, Alsace (near Germany), Provence (SW) and the French Riveria as well as the Loire Valley.
Suggest that you only do TWO countries. You need five or six days each for Paris and Rome.
You probably should take the train, don't try to rent a car if you aren't use to driving in Europe, especially Italy.
There are some MUST see museums, I include the Vatican museum and Sistine Chapel at the top. Also, in Florence Academia (David) and the Uffizi. Do a gondola ride in Venice.