Need help choosing a Travel Pass for Switzerland

Looking at your itinerary I think the
Half fare pass would save you the most money.
The other pass does not have benefits to cover your mountain excursions.

But before you buy take time to read the rules and benefits.

If you want to go through the exercise, make a spreadsheet and list every single trip. The prices are at www.sbb.ch/en, and the Schilthorn round trip is at www.schilthornbahn.ch. If the total is more than 240 CHF (I think it will be) then the Half Fare Card will save money. Keep in mind that the Swiss Travel Pass still only gives you a 50% discount on the Schilthornbahn above Muerren, the Mannlichen Gondola. For the ride down from Kleine Scheidegg (its a train, not a gondola) you only get a 25% discount. The Half Fare Card gets you 50% on everything. I've done these calculations many times, and the Half Fare Card saves the most money 98% of the time.

Thank you for this information. I did a search of my major train connections and it was already 309 CHF so I will definitely be getting the half fare card. I think this will make more sense since we have not fully decided on which mountain excursions we want for sure, and will allow us to be more flexible in that regard. Can you please direct me to the correct link to purchase Half Fare Cards. The website is slightly confusing to me....Would you recommend purchasing any tickets in advance for the month of July? Or would buying train tickets the day before (in country) be best? I just want to make sure we have a train ticket to Zurich airport the day we fly out. Also, between seeing First Mountain, Schilthorn, and Kleine Scheidegg (if you've been there) is there one that stands out to you the most? Thank you so much.

Swiss trains run like city buses, they don't sell out but may be crowded at peak times on popular routes. Reserving seats is not the norm. Just hop on and find a seat. Nothing open? Stand until seats open up. They run very frequently, so they are not normally crowded. People travel when they need to without fretting about schedules.
You can buy Half Fare Cards at the train station when you arrive. You can even download their app and buy tickets with your smart phone and load the ticket on the phone.
Piz Gloria at the top of the Schilthornbahn is pretty neat. I've only been there to ski, so they are all just skilifts to me. But very special nonetheless.

Hiking:
Mannlichen - Kleine Scheidegg Hike (2.5-3.5 miles, 1-1.5 hours, 900 ft. drop) Will need to take
gondola from Grindelwald to Mannlichen, and gondola back down from Kleine Scheidegg to
Grindelwald??)
First Cliff Walk by Tissot
Mountain Views:
Schilthorn and James Bond Exhibit; take train from Grindelwald to Lauterbrunnen. Take the Post
Bus to Stechelberg and then transfer to cable cars for the four segment trip to Schilthorn. (will
need to change cars at Gimmelwald, Murren, and Birg). I assume we can do this same journey
back down as well.

For Männlichen-Kleine Scheidegg, you do indeed take the gondola up at Grindelwald, but to come back down you take the cogwheel train.

The First Cliff Walk requires you to take the lift from Grindelwald to First (very long and beautiful!). While you are up there, why not hike to Bachalpsee? Very easy and beautiful.

When you go to the Schilthorn, you are correct on the routing, but on the way back, consider taking the little train from Mürren to Grutschalp then taking the gondola down to Lauterbrunnen. Makes for a complete roundtrip.

The HFC is a no-brainer for you, but I think you might also benefit from a Berner Oberland Regional Pass. You will get an additional discount on the Pass because of the HFC and a bit more off on the Schilthorn trip. This is a case where you kind of need to do a spreadsheet to be certain. Note the BO Regional Pass also covers the Post Bus.