First timer to Murren this summer, can you help me plan it?

A Swiss Half Fare Card is almost always the biggest money saver pass for your Swiss Travels. Every bus, boat, gondola, funicular, train you take in Switzerland is reduced by 50% with the HFC. If you just can't figure out the exact savings of each travel pass then the HFC is just the simplest way to go.

Dear Lurker, You ask cheapest/most efficient way to accomplish all that?, the second half is easy, just hop the first train from Basel SBB heading in the right direction (Interlaken). Two trains per hour.
The first part, how to pay is difficult.
1) Swiss Transfer Ticket (see below for price comparison) for Basel - Mürren and Mürren - Zürich, buy Jungfraujoch later..
2) Half price card + half price tickets.
3) Swiss pass + reduction for Jungfraujoch.
4) Single ticket Basel - Bern + Berner Oberland Pass + Bern - Zürich

The big question, is what other trips will you be doing around Mürren. I guess up and down the valley a few times?
Plus what after Zürich. Is it Zürich airport you want to get to, or are you going somewhere after Zürich?

Berner Oberland Pass (website: http://www.regionalpass-berneroberland.ch/en ) costs CHF 250 for 4 days (2+3+4+5 July) and is probably overkill.
If you are doing no more trips I think option (1) is your best, if you are doing more travel, a half price card and half price tickets throughout.
Basel to Mürren will cost CHF 80 per person (2nd class full fare) + Mürren to Zürich airport CHF 94, total CHF 174.
With a half price card this becomes CHF 40 + 47 = 87.
A Swiss transfer ticket costs CHF 146. See https://www.sbb.ch/en/home.html for more times and prices.

Other than Jungfraujoch if the weather holds, yes, just hanging around Murren most likely.

We will be staying the one night in Zurich then flying out back home!

Thanks,
Frank