Personally on a short visit I prefer to see one region/city in depth rather than trying to rush all over the place - but that is what I like to do! Both are possible for you,.
If you made Geneva your base for three nights, you could explore Geneva on the arrival day, go to Chamonix on the second, and take a lake cruise on the third. Moving on to Zurich by train you should go to Montreux, take the Golden Panoramic train over to Spiez, then pass through Interlaken and arrive in Luzern. You could spend a couple of hours in Luzern and see just about everything in the town and then go on to Zurich for your last night. Spend the morning in Zurich, walking around the old town (which is very lovely, and much larger than Luzern's altstadt) and then fly home from Zurich in the late afternoon.
My preference would be to stay in the Suisse Romande, flying in and out of Geneva. If you then split your time between Geneva and Vevey or Montreux you would have time to see a lot more of this region - you could include a cisit to the Chateau de Chillon, hike in the vineyards, trip up the Rochers de Naye for a splendid view of the Valais and Vaudois akps, train to the Pays d'Enhaut (Rougemont, Rossinière, Château d'Oex) and even a visit to Gruyères. And then save the German part of the country for another time.