Need help choosing Swiss Train Pass..

I bought my pass in person the day I arrived at the airport in Zurich and Geneva. The multilingual Swiss Rail agents there would be the ones to give you the best recommendations. The counter is open from 6:30 to 22:00.

We are going in early Sept. Similar route, but going from Murren on to Italy. There is no easy answer to the Travel Pass question. You have to do a spreadsheet and list all of the legs, get prices from SBB site, and do the math. With the Travel Pass you can just hop on the train, bus, boat which has alot of value in itself.

Note, the full Swiss Travel Pass covers the entire trip to (boat and rails) Mt Rigi near Lucerne, and Schilthorn from Murren. (Jungfrau is only 25% off with the pass) If you do those 2 excursions, plus your other misc usage, it should just about pay for itself. At least according to the calculations I did for my trip..

Good luck.

3 year old daughter. (From what i have read we don't need to buy a rail pass for her but I would like for her to have her own seat if possible

Yes, under 6 is free (6 to 16 is ½ price, after 16th birthday you are an adult). No issue about a seat. Seats are not reserved, just get on and sit anywhere free.
Trains are very toddler-friendly as she can get up, walk down the aisle, press her nose to the window and go to the toilet whenever she wants. Bring food and drink for the journey. Travelling with a small backpack for such items is normal.

Day 1 - Zurich to Lucerne

I am guessing you are flying in. In which case your starting point is the station at Zürich airport ("Zürich Flughafen"), not Zürich HB (the station in the city centre). Important difference if looking up trains.

Day 4 - Murren to Montreux
. . . Interlaken Ost to Bern to Lausanne to Montreux I think there might be another route but this is the one i hear about the most...

The fastest route is via Bern. The "one you here about" is not via Bern, it is the so-called "Golden Pass" route: Interlaken - Spiez - Zweisimmen - Montreux.

120 train to 50 train - from Montreux to Gruyeres

Not sure what that means.

Swiss Pass
This map shows what is covered by a Swiss Pass: https://www.sbb.ch/content/dam/sbb/de/infotexte/uebersichtskarte-sts.pdf
As you can see, the Swiss Pass covers you to Mürren (both routes) and up to Schilthorn. On the other side of the valley only up to Wengen, above that to Jungfrau it is discount only.
Out of your itinerary, this is the only thing not covered. Everything else is covered, including spur-of-the-moment trips.
Without doing the sums (Don't sue me☺) I think the Swiss Pass is your best fit.
You can buy your Swiss Pass at Zürich Flughafen (airport) station when you land.

For your mountain trips, be flexible. You need a clear day for Jungfrau. If it is not clear, switch days and stay below the clouds.

You really have to price it out for yourself. The trip up the Schilthorn from Mürren in covered 100% by the Swiss Travel Pass. You aren’t leaving yourself much time in the mountains to allow for bad weather. A trip to the Junfraujoch or up the Schilthorn wouldn’t be worth it, if the weather is bad.

Yes, a Swiss Travel Pass covers the lifts and trains to Muerren. You can look at the synoptic map you can download at this site. Click on "Map of validity".
https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-travel-pass.html

Basically, an STP is good for public transportation to any village with year-round residents, which Muerren is. Kleine Scheidegg on the other hand, has no year round residents, other than a few caretakers, so you have to pay extra for that. One exception is that the Swiss Travel Pass is good to the top of the Schilthornbahn, at least for this year.

Here is a step-by-step process to find the most economic pass to get, or not get, if you are handy with spreadsheets.
https://www.myswissalps.com/train/ticketspasses/practical/chooserailpass

It sounds like the Sept. 30 is the date you fly home, with no pass coverage needed. That leaves the 5 consecutive travel days that you specified. I would choose the Swiss Travel Pass. However, the best-fitting options are for either 4 consecutive days at about $278 per adult, 4 days during a one-month window for $319, or 8 consecutive days for $413.

I'd be leaning toward the first option, plus ticket from Zurich airport to Luzern for $30 per person, on the assumption that you'll fall asleep soon and not use the pass for boat trips, museum visits, or mountain rides on Day 1. If you think your covered activities on that day would actually add up higher than plans for Day 5, then you could choose a different start date. Note that the consecutive-day pass is pre-activated for a specific 4-day period at the time you buy it, whether online or in station.

Thank you all! I think i'm going to buy the Swiss Travel Pass.

Is Murren really not stroller friendly ? i'm really sad if this is true. I really wanted to stay here, and not in the valley.

The main roads of Muerren are paved and not used by many vehicles, so I think it's fine for a stroller.

OOH excellent!!! thank you!!! i was worried it was cobblestone streets. Are you from the area? are their any nice hiking trails we could do with a stroller?

linnetteh, within the villages no problem with a stroller. And Mürren is car-free.
If you want to start hiking between villages, those paths are gravel and not friendly to a stroller with small wheels.

Photo of street in Mürren: https://alpinetraveler.com/wp-content/uploads/2017/06/Murren.jpg
Photo of hiking path outside Mürren: https://alpinetraveler.com/wp-content/uploads/2014/11/curving-toward-Murren.jpg

WOW! thank you Chris for the info! Your pictures got me super excited!!! i can't wait to see those beautiful mountains!! :)
those hikes look a little scary for us to be hiking with a 4 year old, i would be scared she falls off the edge. ah! i hope there are other hikes in the area where she would be able to walk with us and not be scared.

"Mürren is car-free."

Just be aware that car-free is not the same as vehicle free. There are service vehicles (kind of like tractors) in the car-free villages, during both the day and the night. I learned - quickly - that you can't just walk down the middle of the street without looking. However, there aren't that many service vehicles, and it's certainly different from a road with constant car traffic.

Yes, some walks will have minimal barriers, but others will not have any problems on that score.