Zurich to Murren July 2 Best route & fare?

The Half-Fare Card for visitors is a better deal than paying full fare on this trip.

Or, a short visit is no barrier to using a Swiss Travel Pass, since they do come in versions for 3 or 4 consecutive days. In addition to your two main transport routes, they also cover lifts to the top of the Schilthorn, and half-way up the opposite side of the valley, plus discounts above Wengen or Grindelwald. Day 4 (adds an average $45 per person) could be used for museums and city trams in Basel, and the airport bus (about $8), but you probably don't have any larger expenses there. Check whether your hotel provides any city card that covers the trams.

The shorter train ride from Zurich is via Bern, but the more scenic route is via Luzern (1 - 1.5 hours more). See www.sbb.ch or Looking Up Train Schedules and Routes Online gives you the Deutsche Bahn train schedule link and tips for using it. You can request, for instance, from Zuerich airport to Muerren BLM (train station) via Luzern.

Take the more scenic route especially if the weather (visibility) is good.

Actually, the Half Fare Card saves the least if you go via Luzern. Assuming you will take a ride up to the Schilthorn, You will pay 1.60 CHF per person over doing nothing. A Swiss Travel Pass for 3 days each will save about 22 CHF per person, mainly because the boys get a Youth discount for the Travel Passes.

I believe if you stay in a Basel hotel, you will get hotel cards that will get you free use of Basel transit including the bus to the airport.
https://www.basel.com/en/BaselCard

I too would recommend the Zurich to Lucerne to Lauterbrunnen route rather than going thru Bern. It is more scenic and changing trains in Bern is not pleasaurable - like wise going Zurich-Lucerne-Lauterbrunnen costs less than going thru Bern.

All routes and times can be seen at www.sbb.ch/en

Origin: Zurich Flughafen
Destination: Murren BLM

In the "via" box, type Luzern to go that way. Otherwise it will show you trains through Bern, because it is faster that way.