Our 15 days Swiss Itinery in OCT- comment needed

Hello Swisslovers, and welcome to the forum! I'd definitely recommend a 15 day Swiss Saver Pass for your itinerary. You'll be traveling almost each day and you plan on making quite some long (and therefore expensive) train trips. The Swiss Saver Pass offers free travel throughout the country, on nearly all routes you mention. Mountain transportation (such as Schilthorn and Jungfraujoch) is discounted. Please click the link 'Overview of the network on which the Swiss Pass is valid' at the Swiss Pass page to take a look at the routes on which the Swiss Pass offers free and discounted travel.

Your Swiss Saver Pass will serve as your train, bus and boat ticket: you can simply get on and off board whenever you like, without having to buy additional tickets, which is very convenient (again, for mountain trains and cable cars additional tickets are required). Seat reservation isn't required, unless you want to travel by special panoramic trains, but they don't seem to be included in your itinerary.

As for your travel scheme: personally I'd aim at taking the shortest and most efficient routes. You could make more of a round trip by changing the order of towns. My first idea would be to follow this route: Zurich - Lucerne - Lugano - Zermatt - Geneva - Interlaken (you could take the beautiful Golden Pass route between Geneva and Interlaken) - Zurich. This saves you from having to make the long trip from Zurich to Lugano first, and then travelling all the way back to the north to Lucerne again. Please take a look at the map I mentioned above to see what I mean. You can plan your trips with the aid of the Swiss timetable.

I hope this answers your questions. Good luck on your preparation!