1st class or 2nd class train tickets

No.
Second class is perfectly adequate. The difference is 2+2 seating in 2nd class, and 2+1 in 1st class.
See the photos here: https://www.seat61.com/Swiss-trains.htm#What%20are%20Swiss%20trains%20like
The rest of that page should answer all your other questions about Swiss trains.

If I may also comment on your plans:

• "We plan to start in Zurich" - does that mean you are flying into Zürich airport, or arriving by train from another country?

  • If you are flying in, unless you are arriving really late, you can catch a train from the airport and get most if not all of the way to St Moritz on your arrival day.
  • If you are arriving by train, you do not have to travel via Zürich. Depending on where you are coming from, and where you want to spend your first night, the quickest route may not be via Zürich.

• "travel from Zermatt to Geneva"

  • Why Geneva? Geneva is out of your way, and like Zürich not one of places to recommend a first trip. Both are big cities, and you come to Switzerland to see mountains, not cities.

• "Geneva to Bern, Bern to Lucerne"

  • Bern is nice, worth a day. But you are skipping the best bit of Switzerland, the Berner Oberland. You need to spend some time there. Easy to go Bern --> Berner Oberland, then --> Luzern.
  • The places to recommend for a first stay in the Berner Oberland are Mürren, Lauterbrunnen, Wengen or Grindelwald. Here is the official website with what to do, and hotels: https://jungfrauregion.swiss/en/summer/

• "and back to Zurich." No need to stay in Zürich. From Luzern it is only 70 minutes by train to Zürich airport. Unless your flight is really early, you can say your last night in Luzern.

I will be flying from Atlanta, GA and traveling with my 86 YO mother. I think it would be in our best interest to stay overnight in Zurich. We will leave early the next day to head to St. Moritz. I was questioning the Geneva leg of our trip and maybe stay in Lausanne instead as my mother is interested in the Chocolate/Cheese/ Wine tours in this area. I have thought of either taking an organized tour or perhaps renting a car and doing a self guided tour. Most tours give you lots of time at the Cailler and Gruyeres but only a visual of the wineries. Mom and I like the wineries!
Bern, my mom wants to ride the Gelmerbahn 360??
Lucerne, I had originally planned to go to Jungfraujoch but her doctors recommended against this. We've decided to split the difference and are taking a day tour doing Mt Pilatus/Lake Cruise/ Cog Wheel/Cable Car .
The trip back to Zurich was recommended as we have to be at the airport very early in the AM for our flight.

I did the math for 1st vs 2nd and 2nd is a savings of $600 each. That's a no brainer...2nd class it is!
Anymore input on my explanation above would be appreciated.

traveling with my 86 YO mother. I think it would be in our best interest to stay overnight in Zurich.

A compromise: Chur
It is on the way to St Moritz, and puts you in the Alps.
Zürich Flughafen (airport) to Chur: 2h25. A direct train at 23 minutes past every hour (plus 2 more requiring a change)
So it is still a "one seat" ride from the airport, and you get to see some mountains and lakes. Sit on the left of the train.
The Glacier Express starts from either Chur or St Moritz

And, between Bern and Luzern, do not take the fast train, instead route take the route via Interlaken. It goes through the mountains (over the Brünig Pass) instead of around them.

2nd class on train is similar to business class on an airline. Decent seat spacing. IMO, the main advantage to first class is the wider seats. If there is a increase in leg space it has not been noticeable to me. Distance between seats is about the same.

First class trains cars have (almost always) 2+1 seats instead of 2+2. They also tend to be a little quieter and emptier.

The Excellence Class is a bad price/experience proposition in my opinion, but preferences might vary.

When you purchase a ticket from say Zermatt to Lausanne, can you get off the train in Montreaux and get back on later to continue to Lausanne?

When you purchase a ticket from say Zermatt to Lausanne, can you get off the train in Montreaux and get back on later to continue to Lausanne?

Yes, as long as:
a) Where you get off is on the direct route to your final destination, not a longer route.
b) You buy a normal ticket from A to B, not a discounted "Supersaver" ticket, which are only valid on the train listed on the ticket (details of Supersaver tickets here: https://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/supersaver-tickets.html )
c) Both legs are on the same day.

• Of you have a pass, this is all academic as you can travel when and where you want.
• There is nothing to stop you buying TWO Supersaver tickets, Zermatt to Montreux and later Montreux to Lausanne
• Zermatt to Lausanne costs CHF 81 (2nd class, no discounts), Zermatt to Montreux is CHF 74, Montreux to Lausanne is CHF 13, so the difference is only CHF 6.
  • Supersaver fares will save you money off those prices.