Travel from Zurich to Murren

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This is discussed frequently here, so join the club of confusion. It helps knowing if you are planning to go on additional modes of transportation, including boat rides, up to Mt Rigi, etc.
Download the SBB app and play around.
Basically you need to pencil out the differences between full price , half price with the Half Fair card, and Swiss Travel Pass. (The latter is on sale thru May 15. ) Note that the prices shown on the SBBsite are assuming you have a Half Fare card.
Have a great trip!

We will travel from Zurich to Murren, and spend three days there, and then return to Zurich via Bern and Luzern.

The route back to Zurich is via Bern OR Luzern. Doing both is a bit overkill. Suggest if you want to visit Bern, do that for an afternoon on the way to Muerren, then go from Muerren to Luzern on the way back and spend the night. It is a direct train from Luzern to Zurich airport (assuming you are flying out from there).

I don't think you have enough time for Bern.

I'd go to Luzern on the day before the flight, using the extremely scenic Brünig pass cog railway - the normal railway between Luzern and Interlaken. Sit on the right which will become left when the train changes ends in Meiringen. Enjoy.