First, you’ll want to do this trip via train. Renting a car will be very expensive with the country drop off fees and most of what you’re doing in Switzerland is in car free areas. The cities in Austria have challenging parking and getting a private driver would be extremely expensive with your route. Train info below after the itinerary suggestion.
You are correct to start in Switzerland in the mountains and end in Austria. I recommend Wengen for a first time visit. It’s car free, charming, beautiful mountain views and well situated for day trips within the area. It has grocery stores, shops, restaurants & there are many good hotel options. However, for a longer stay you could also consider a chalet apartment rental (look at interhome, e-domizil, airbnb, Wengen Apartments, Alpine Holiday Services, etc.) — just make sure to get a south facing balcony for best views and note that Wengen is built on the side of a mountain so if you get too far downhill from the train station you’ll have a bit of a “hike” to/from the train/shops. For hotels, the Maya Caprice is well located and nice. If you want to stay in a true authentic Swiss village that still has many chalets from the 1600s and is connected via cable car or bus, then Murren has the best views in the area. It takes around 20 extra minutes to connect out for day trips to the further region, but there is a ton of hiking and biking right around there. They also have chalet apartments or depending on your budget, the nicest hotel is the newly renovated historic Murren Palace. I don't love Lauterbrunnen, especially in October as the steep cliffs make the valley go in to deep shadow in the afternoon, making it colder feeling and less picturesque for "cocktail hour on the balcony with a view after a long day of hiking and sightseeing" :)
I’ll make an assumption of 18 nights in my suggestions…
Fly in to Zurich > Wengen 6 nights > Zermatt 3 nights > Pontresina 3 nights > Innsbruck 3 nights > Salzburg 3 nights > Fly out of Salzburg or Munich
Here is a day by day. Obviously some of it is weather dependent, but it gives you an idea of what you can accomplish in a day….
Day 1 - Zurich Flughafen (airport) > Wengen (3 hr train) - explore village
Day 2 - Mannlichen + easy scenic walk to Kleine Scheidegg + optional Jungfraujoch
Day 3 - Murren/Schilthorn/Gimmelwald
Day 4 - Lake Thun boat ride to see castles (Spiez, Oberhofen, Thun)
Day 5 - Lauterbrunnen Valley e-biking (up to Trachsellauenen if you have the fitness ability)
Day 6 - weather buffer day for all of the above (or places like Schynige Platte, Grindelwald First, biking Grosse Scheidegg, etc.)
Day 7 - Wengen > Zermatt (3 hr train) - explore village
Day 8 - Gornergrat
Day 9 - Glacier Paradise, weather buffer for Gornergrat
Day 10 - Zermatt > Glacier Express to Samedan and on to Pontresina for a base (8 hr train ride)
Day 11 - Pontresina relax (bike or hike options)
Day 12 - Bernina roundtrip to Tirano & back to Pontresina to sleep (4.5 hr roundtrip train ride)
Day 13 - Pontresina > Innsbruck (4 hr bus/train ride) - this will be a very scenic ride as well through a very quiet part of Austria
Day 14 - Innsbruck exploration
Day 15 - Innsbruck mountain excursion
Day 16 - Innsbruck > Salzburg (1.5 hr train)
Day 17 - Optional day trip to Salzkammergut (Hallstatt, etc.) or Hohenwerfen or Konigsee
Day 18 - Salzburg
Day 19 - Fly out of Salzburg or Munich (1.5 hr train)
Rest of my advice continued in next response, as this ran out of space :) ......