Hello hienyville
Provided you are spending the most of your time in the Berner Oberland, the Berner Oberland Pass would have been the travel pass of my choice. Nevermind, you can also travel with the Swiss Travel Pass, it grants you, what concerns free public transportation, similar benefits in that area. Plus, it covers your journeys from/to Zurich.
Just one thing: if you are on a budget, I wonder why you have chosen Zürich as a first base, knowing Zurich is the most expensive city in the world. It would have been advisable to stop at Lucerne, on your way to Lauterbrunnen. It has moderate prices and is more Swiss. Zurich is simply an international place, so are the people and the cost.
Kind regards,
Roland