2 week Switzerland and Italy trip

Mid-Sept is lovely in the Lauterbrunnen Valley, so good timing. Certainly spend at least 4 nights as this will be your favorite place in the entire trip I think.

Heading to southern Italy is OK, but you will have a long day the day of transfer. When we lived there, we did Lauterbrunnen back to Rome by train several times and it is easy. You will want an EC out of Spiez to Milan and change there for a high-speed train to Rome.

Alternatively, consider spending more time in Switzerland (look at Pontresina) or stick to northern Italy: the lakes region, Venice, Verona, etc.

We loved our stay in Pontresina! Motif painted houses, charming.

Laurel, thank you for your feedback! We are considering flying into Zurich and staying in Switzerland for four nights. With low flight costs right now, we feel it may make sense to fly to Rome from there. It looks like flights departing from Basel to Rome are the cheapest. Any experience with Basel airport versus Zurich? We would then spend five nights in the Sorrento area( after 4 in Rome )and then fly home out of Naples. Thanks.

We never fly in Europe (well,once, from Rome to Sicily) so I cannot help with airports.

I haven’t flown from Basel Airport but would have no issues with choosing it. Frequent shuttle buses connect there from Basel main train station, also shown on train schedules when you search through SBB or DB.

Re Basel airport.
Basel (as well as Geneva) is a base for cut price airlines (EasyJet etc.). Zürich is not, mostly "full price" airlines there.
Basel airport is the same time from the Berner Oberland as is Zürich airport, Geneva takes 40minutes longer.
If you want to fly to Rome, Basel is the obvious choice.
The only slight disadvantage is that it has no direct rail link, it has a shuttle bus from outside the station, and the bus sometimes gets crowded. Passes are valid on the bus, and you can buy through tickets from any Swiss station to the airport including the bus.

Don't think you're packing too much in - 4 nights Switzerland, 4 nights Rome. This leaves you 4-6 nights right? I would fly because it's likely to take a long time to get from Murren to Rome (check out www.eurail.com - it's like 18-20 hours from Interlaken). We were there in July 2017 and loved the hiking. We based out of Wengen for 4 nights and felt we made the right choice comparing Lauterbrunnern, Murren and Wengen.

it's likely to take a long time to get from Murren to Rome (. . . . it's like 18-20 hours from Interlaken).

It's a long time, but not that long. Actually about 8-9 hours from Mürren. Use the websites of the actually rail companies to check times, not all reseller sites show all trains.
I looked on SBB (Swiss Federal Railways): https://www.sbb.ch/en

Note times in Italy are only published up to June so far. You need to look at a date in May to see what the times are. A lot of trains are currently temporarily cancelled. Looking for the next few weeks will not show the "normal" train times.

I stand corrected. With only 8 hours on the train it's worth a look.