Hello Leaghoillaix16
Travelling with such a large group certainly needs an accurate upfront planning.
Group tickets might be an option, however, they need a prearrangement.
https://www.sbb.ch/en/tickets-offers/tickets/group-tickets-switzerland.html
As part of individual tickets, the Swiss Travel Pass could be an option. It offers reductions for youth, as well as the free Swiss Family Card for your 15 yrs old.
Another option is the Swiss Half Fare Card for all travelers, plus individual point-to-point tickets or Saver Day Passes. Again, if a parent holds the Swiss Half Fare Card, there is the Swiss Family Card for your 15 yrs old.
In my opinion, it would be the best if you seek advice with an Rail Travel Center agent upon your arrival to dicuss the ticket option for each of your excursion.
Personally, I wondered why you have chosen Zurich as a base. If you gonna stay in Switzerland for the first time, Lucerne would have been the better choice, as it is much more Swiss. Also, Interlaken is okay as a travel hub, however, it isn’t particularly Swiss; it is host to primarily tourists from Asia, India, and the Middle East. It has a lot of Asian restaurants. You should plan mountain excursions to Grindelwald / Wengen / Mürren / Schynige Platte, or boat cruises on Lake Brienz and Lake Thun.
There are two excellent travel forums, myswissalps.com and the English speaking Travel Forum of TripAdvisor Switzerland. Both are moderated by locals and they could give you in-depth advice on travel plans and places to visit. Here in the SBB Community we remain at your disposal for any further ticket and public transport travel related questions.
Best regards,
Roland