Train route recommendations

Besides the fact that the Gotthard Panorama Express is the slow (but more scenic) way, when there is shortcut underneath the mountains (Gotthard Base Tunnel), you will also have to back track to Luzern to use these routes. The fastest way is a train to Spiez and there you can get a direct train to Milan that uses a couple big tunnels, the Loetchberg Base Tunnel and the Simplon Tunnel.
Use www.sbb.ch/en to research the routes to Milan. That will show you the fastest way. To compare the other way, put in Goeschenen in the "Via" box.

Going via Spiez can be done in 3 hours and 10 minutes, going via Goeschenen takes 7 hours and 10 minutes.

From Interlaken West train station you’ll need to transfer in Spiez (30-minutes) to Milano Centrale train station (2h 45m). There's a direct train from Milano Centrale to Firenze S.M.N. (1h 45m).
The Gotthard Panorama Express runs between Luzern to Lugano. The first leg, Luzern to Flüelen is by boat where you’ll then board the train. The next stop is Bellinzona which is near Lugano. The area between Bellinzona and Lugano is the least interesting according to: https://www.myswissalps.com/gotthardpanoramaexpress/gettingthere.
The train from Interlaken Ost to Luzern takes 2h and requires a connection. The train from Interlaken Ost to Flüelen is even longer.

The first leg (Interlaken to Spiez) is non-stop

Except for some charters there are no non-stop trains between Interlaken Ost and Spiez.

I've been on that route dozens of times and I speak from experience and knowledge of reading the detail in timetabels.

All trains, including locals, French TGVs, German ICEs, Swiss expresses and regionals, call at both Interlaken Ost (the end of the line, where the connections are made onto the narrow gauge towards Luzern and Lauterbrunnen and Grindelwald) and Interlaken West on the way to Spiez and parts north. Local commuter trains on the same route not only call at Interlaken West but several other various local stops along the lake.

Don't be like me and get off at the stop number you think is right. I did that on a local train between Venice Mestre and Venice Santa Lucia many years ago. I realized we had a problem when we stopped and the only people to get down were my wife and I - we jumped up like lightning just as the doors were closing after throwing the luggage back on. oops. Listen for announcements and read the display screen by most doors now and in the each seating area.

The train from Interlaken Ost to Luzern takes 2h and requires a connection.

No change of train is needed on the very scenic Interlaken Ost to Luzern via the Mairingen and Brünig Pass route. The train does indeed change ends at Meiringen but you don't need to leave your seat, unless you want to sit on the opposite side of the table (advice, sit on the right side of the train leaving Interlaken Ost to get the best views of Lake Brienz, the town of Brienz, the waterfalls, the mountain views (you'll be on the left side after you change ends in Meiringen (the home of Reichenbach Falls where Sherlock Holmes has his battle - there is a funicular up the falls)) and then the mountain lakes and eventually Lake Lucerne (Vierwaldstättersee in German). A fabulous route which I have ridden many times and recommend to everybody. Heck, several sections are on the cogwheel rack it is so steep and scenic.

You could I suppose take the longer way around, and much less scenic, via Spiez, changing at either Bern in 2H01 or at Bern and Olten in 2H25 but why would you want to? More hassle, slower, way less scenic.

EDIT: I see the post quoted has changed. My advice remains the same.

If you want a compromise on the short way via Spiez, put in Kandersteg in the "Via" box. Then you will be routed on the more scenic "Loetschberger" train that goes mostly over the mountains by passing the Loetschberg Base Tunnel. That way will take 4 hours and 10 minutes, 1 hour longer than taking the direct train to Milan. You will have to change trains at Domodossola, Italy, where the "Loetschberger" terminates. Sit on the right side of the train for the best view as you descend from the old (shorter) Loetschberg Tunnel to Brig.

Since the OP has stated that he will be traveling from Luzern to Interlaken, he should sit on the right side of the train leaving Luzern, so the he will be on the left side when the train changes directions at Meiringen for the leg into Interlaken with views of the lake.

Except for some charters there are no non-stop trains between Interlaken Ost and Spiez.

Nigel, if you don’t see “intermediate stops” in DB then it doesn’t mean it’s nonstop? https://reiseauskunft.bahn.de/bin/query.exe/dn?revia=yes&existOptimizePrice-deactivated=1&country=DEU&dbkanal_007=L01_S01_D001_qf-bahn-svb-kl2_lz03&start=1&protocol=https%3A&REQ0JourneyStopsS0A=1&S=Interlaken+Ost&REQ0JourneyStopsSID=A%3D1%40O%3DInterlaken+Ost%40X%3D7869004%40Y%3D46690502%40U%3D80%40L%3D008507492%40B%3D1%40p%3D1623428175%40&Z=Spiez&REQ0JourneyStopsZID=&date=Mon%2C+14.06.2021&time=19%3A09&timesel=depart&returnDate=&returnTime=&returnTimesel=depart&optimize=0&auskunft_travelers_number=1&tariffTravellerType.1=E&tariffTravellerReductionClass.1=0&tariffClass=2&rtMode=DB-HYBRID&externRequest=yes&HWAI=JS%21js%3Dyes%21ajax%3Dyes%21&externRequest=yes&HWAI=JS%21js%3Dyes%21ajax%3Dyes%21#hfsseq1|44.026392145.1623715793

@ MaryPat: When I click on the link you posted, then click on "Details", then "show intermediate stops", it shows that the train stops at Interlaken West on the way to Spiez.

Thank you, Sam, I edited my original post.

https://www.sbb.ch/en/station-services/at-the-station/railway-stations/trafimage/trafimage-karten.html

Download the network pdf to see Switzerland's trainroutes on a map.

For the Lucerne to Interlaken Ost route take the Golden Pass train. The views are awesome.

The Golden Pass trains have big windows. It is also good to know that a few years ago the Zentralbahn changed all its ordinary local trains on that route for modern airconditioned low floor cogwheel units with floor to ceiling windows even in second class.