Geneva > Zermatt > Zurich

Buy a Half Fare Card in advance, specifying the start date as your arrival date. You can buy on arrival but it is nice to buy in advance on the SBB website and have it on your phone in the app. Be sure to create an account before you make the purchase and download the app to your phone. Then the HFCs will be on your app for easy display when needed. Buy point to point tickets with the app which will then apply the half fare discount automatically. No need to buy the point to point tix in advance unless you want to commit to a Saver Fare, which is a commitment as it is non-refundable so be careful. Do some: research at https://www.sbb.ch/en.

I would choose Montreux over Geneva for your arrival stay and I would choose Luzern over Zurich as it is only an hour from the Zurich airport.

Here is a way to save a bit more. Do not buy the Half Fare Card as it costs 120 CHF per person. Doing GVA>Montreux>Zermatt>Luzern>ZRH is 266 CHF full fare tickets per person, So with the Half Fare Card, you will pay 120+133= 253 CHF, saving you only 13 CHF per person.

The other way, is to buy now Saver Day Passes, costing 52 CH each for the days you are arriving in Zermatt and the day you are departing. Then just buy full fare tickets for GVA>Montreux (37 CHF) and Luzern>ZRH (31 CHF). so now your cost will be 37+52+52+31= 172 CHF. So that saves 94 CHF.

You have to buy the Saver day Passes now, as the prices increase as you approach your travel date. They are for a specific travel date, which you know because you already have lodging booked in Zermatt for those days (I assume).
https://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/day-pass/saver-day-pass.html

Would it make a difference if we were just traveling from Geneva -> Zermatt then Zurich and skipped the stops in between with getting any sort of discount card and just purchasing the point to point tickets when there?

If you just went directly GVA>Zermatt and then Zermatt>ZRH, then that would be just 2 Saver Day Passes at 52 CHF each per person.

The Saver Day Pass allows unlimited travel in Switzerland on a given day, so you can take any train on your arrival day as long as your flight arrives on that day.

Montreux in December could have terrible weather/fog, rain etc. so I would head straight to Zermatt, personally!

Stay in Lucerne, not Zurich. Lucerne is much more charming. If your flight out of Zurich isn't too early, remain in Lucerne, as it's an easy 1+hr train directly to the Zurich airport.
Safe travels!

So it would be recommended to get to Saver Day passes for the two days taking trains for 52 CHF (which an additional ticket doesn’t need to be purchased for this train ride) instead of the point to point ticket the day of? is it less expensive if done this way?

Yes, no additional tickets needed with the Saver Day Pass. It is essentially a 1-day Swiss Travel Pass. A point-to-point ticket from Geneva airport to Zermatt is 102 CHF and a point-to-point ticket from Zermatt to Zurich airport is 134 CHF. So obviously 52 CHF is a better deal. Note, the prices go up as the travel day approaches. I am already seeing prices of 61 CHF for some days in early December, so the sooner you buy, the cheaper the price.

Thank you so much!

It says Saver Day Pass you can travel throughout Switzerland for a day on all routes in the GA area from as little as CHF 29 with a Half Fare Travelcard and from CHF 52 without a Half Fare .. this is correct right one pass should allow me to get on any train ride with the pass not a specific train ride

Correct. Like I said, it acts like a 1-day Swiss Travel Pass. Note that prices increase as your travel day approaches, and they are completely nonrefundable. They must be used on the specific day they were purchased for, up to 5 am the following day.

For instance, you see that one purchased today for use tomorrow costs 119 CHF, for use next Thursday costs 88 CHF, 2 weeks form now costs 79 CHF, etc until you get far enough out that the price drops to 52 CHF, which is the lowest price for one without a Half Fare Card. The earlier you buy, up to a point, the lower the price. So only buy when you are absolutely certain you will travel that day.

Will having something lile the Half Fare card benefit for any travel once in the locations we are going to ? The saver pass makes sense from getting to one location to the next ( we will only be going from Geneva-> Zermat-> Zurich and taking a day trip to Lucerne) but once we are in each of these locations how is it best advised to get around ? Thanks so much!!

The Half Fare Card only saves you money if you have if you have more than 240 CHF worth of full fare tickets per person. For instance, if you were in Zurich and took a day trip to Luzern, the full fare ticket is 25 CHF each way per person. So 50 CHF. If you had a Half Fare Card it would be 25 CHF, but then you would have paid an additional 120 CHF for the HFC just for that, it would cost you 145 CHF rather than 50 CHF. It also depends on what other things you want to do in Luzern. Take a boat ride? Go to Mt Pilatus?

BTW, have you bought Saver Day Passes yet? Also, I see that SBB has announced a price increase effective Dec 10 for all ticket prices, although the increases will not be effective until Jan 1.

Saver Day Pass from Geneva to Zermatt is 52 CHF
Point to Point ticket from Geneva to Zermatt is 33 CHF

Point to Point makes more sense unless you’re saying these Point to Point tickets to increase closer to the date?

Not only that, but I bet that 33 CHF SuperSaver Ticket is only available with the Half Fare Card. Without the Half Fare Card, it will be 66 CHF. A true point-to-point ticket full fare is 106 CHF. The Saver Day Pass allows you to take any train or routing that day.