It sounds like a nice trip!
Montreux is in the western portion of Switzerland and Chur is in the east, with Zurich and Luzern pretty much in the middle. The logical order of travel, to my mind, is Zurich to Montreux to Lauterbrunnen/Wengen to Luzern to Chur.
I have some suggestions for routes and a map of the Swiss rail system, with scenic routes highlighted, so you can follow.
https://cdn-doc.myswissalps.com/docs/default-source/rail-network-maps/swisstravelpass.pdf?sfvrsn=7788603a_56
For Zurich to Montreux, you may as well take the faster route via Bern, as you will be using the scenic Golden Pass route from Montreux to Interlaken (for Lauterbrunnen) and Interlaken to Luzern. These are ##4 and 7 on the map.
From Zurich airport to Montreux you can take a train directly from the airport station to Lausanne, changing there for the short journey to Montreux. Total travel time is 3 hours. This Intercity train stops in Bern on the way to Lausanne, an hour and 20 minutes after leaving the airport. So depending on the time of arrival at Zurich Flughafen, an overnight in Bern instead of Zurich may be an option. Bern is a smaller, less “business-oriented” city, with nice hotel options within walking distance of the train station. They tend to be less expensive than downtown Zurich hotels.
From Montreux to Interlaken Ost, you are on the scenic Golden Pass route, and you have a choice of the named train with panoramic cars (reservations mandatory), or the regular regional trains that ride the same rails. At Interlaken you change to the local train to Lauterbrunnen, changing again there for the little train up to Wengen. The train between Interlaken and Lauterbrunnen splits into two sections, with one going to Grindelwald and the other to Lauterbrunnen, so check the markings on the platform for which section to board.
From Interlaken to Luzern you will be back on the Golden Pass route. Sit on the right side for views of the lake (Brienzersee) and the castle-like Hotel Giessbach across the way.
From Luzern to Chur, you have some choices. The “standard” way is to take a train northeast to Thalwil, changing there for the train to Chur ( some will have you change at Zurich). The “scenic” option is to take the Treno Gottardo (train);or Gotthard Panorama Express (boat plus train) south to Göschenen, changing there for the short journey to Andermatt, where you can catch either the Glacier Express or a regional train straight to Chur. The Glacier Express is direct; if you take a regional train there will be one change at Disentis.
If you look at the map you will see that the north-south Gottand line and the east-west Glacier Express appear to cross one another right around Andermatt. They do, but they do not intersect, as the Glacier Express runs on the surface and the Treno Gottardo runs underneath Andermatt in a tunnel (the dashed line on the map).
Timing the boat option is a little tricky, and the Gotthard Panorama Express runs only once a day, with the boat departing Luzern at 11:12. You arrive at Flüelen for the train continuing south at 13:55, which will be too late to catch the last Glacier Express of the day at Andermatt. But there are later regional trains that will work.
Or you could duplicate the GPE experience by simply taking the boat plus Treno Gottardo. The first boat departs Luzern for Flüelen at 9:12 am, arriving at Flüelen at 11:55. The Treno Gottardo comes through this station at 12:15, 13:15, etc. so you could take the first one, or stop for lunch. The Glacier Express stops in Andermatt at 12:54 and you won’t make that, but you can certainly make the 15:54 train. Be sure to check the schedules for your actual dates, however, as sometimes the schedule has fewer trains early in the season.
Or you could just take the Treno Gottardo from Luzern and skip the boat. This train departs Luzern at 9:18 and 11:18, on the current schedule.
