Where to stay the first part of October, Lauterbrunnen or Wengen?

If you want to stay in the area for 6 nights, then pick one; there's no advantage to doing 3 nights in one and 3 in the other. Lauterbrunnen is a litte more central and busier, but Wengen has better views. Don't fret because both are great, so you can't go wrong.

I was planning a cable car trip, taking in the scenery and that is all
we have planned right now.

Seriously, what you have planned is all the planning anyone needs to do for that region.

Consider going up to the Schilthorn and Jungfrau, both amazing.

If it's open in October, the walk from Mannlichen to Kleine Scheidegg is easy and spectacular.

I'd choose Mürren -- but views from Wengen are supposed to be spectacular too. Will you be getting a Half Fare Card or other pass to reduce your train and lift costs ? We came out about even on 3 days Lausanne-Mürren-Lausanne train tickets plus Schilthorn plus train/bus to Lauterbrennen for the inside waterfalls on a cloudy day.

We like Lauterbrunnen because it is easier to go to both sides of the valley. It is a transportation hub. Also easy to arrive, depart, go to the lakes and beyond.

We have stayed in Muerren and that is, IMO, preferable to Wengen as Muerren gets more sun and has the drop-dead views of the 3 peaks. But after 4 stays, Lauterbrunnen is our favorite due to access. Also, Wengen is super quiet in October. Hard to find a restaurant. There are more in Muerren and Lauterbrunnen.

We will be in Lauterbrunnen again Sept 25-Oct 2. Can't wait!

As Laura said, I’d stay in Murren. Most beautiful and amazing of them all. We’ve stayed there on two different trips, can’t get enough of it.

We stayed in the Berner Oberland for 4 nights in July 17. I recommend Wengen because of its central location, beautiful views, and charming downtown area. Lauterbrunnen was more spread out, not as quaint, and not up on the mountain. Murren was beautiful but seemed less commercial than Wengen - plus it was at the far end above the valley. I would stay in Murren before Laterbrunnen.

Must dos:
Take the cable car up to the Mannlichen and then hike down to Kleine Scheidegg and on down to Wengen;
Take the cable car up from Laterbrunnen and hike to Murren and then down to Gimmelwald - then take the cable car down from there and hike back through the valley to Laterbrunnen;
Eat, drink and be merry!