Which itinerary is the best for the first-time visitor to Switzerland?

Skip Zürich, spend the time saved in the mountains.
From Luzern, the mountain day trip to do is Titlis ( www.titlis.ch ). This is a higher mountain than Rigi or Pilatus. It has a small glacier at the top you can go in and over. See the website.

When you are travelling between Luzern and the Berner Oberland (via Interlaken Ost), whichever direction you do it in, make sure you take the scenic Brünig Pass route (via Meiringen).
Bern is actually easier to get to from Interlaken than from Luzern.

For route planning, use the Swiss Railway map here: https://www.swisspasses.com/railpass/overviewmap_en.pdf

For tickets there are actually 3 options:
1) Normal tickets.
2) Half price railcard and half price tickets.
3) Swiss Pass, which will cover the normal trains, but only give you a discount on mountain railways (Titlis, cable cars above Mürren etc.)
You will have to do the arithmetic yourself to see which is best.

The best place for rail times and prices in Switzerland is the Swiss Federal Railways website: www.sbb.ch
I suspect you may not have been using the SBB site, because you quote time in AM and PM, and Swiss railways (and every other transport company in Europe) uses the 24 hour clock.

I agree, skip Zurich. Nothing much there, at least compared to Luzern or Berner Oberland.
Further, if you have an extra night, definitely stay in Berner O.
Here are 3 easy trails where you can't go wrong:

There are loads of great trails in the area, but 3 that I consider "classic",
and they follow the 3 great ridges. The first goes
from (Lauterbrunnen cable car to) Grutschalp to Murren. From Murren one can also hike uphill on a diagonal from the
Murren cablecar station, and eventually end up at the restaurant at
Spielbodalp. There you can get a drink and sit at a picnic table and watch the
cows. You can see that trail and others here:
http://www.gimmelwald.com/pics/gimmelwald/hikemap.jpg

The second goes from Mannlichen to Kleine Scheidegg. The walk itself is
about 2 hours, and we save this for the sunniest day, because of the panoramic
views. (Leave in the morning--most afternoons the peaks cloud up!) Take the
train from Lauterbrunnen to Wengen, then a 5 min walk to the cable car
station, where you take the cable car up to Mannlichen. Once up, you can look
left at a 30 min up and back trail to a lookout point. If you look right
there is the main tra‎il that leads toward the Jungfrau mounta‌in, which takes
1.5 hrs and you end up in Kleine Scheidegg, where you can catch a train down
to Wengen and finally Lauterbrunnen. Great panoramic views all along the
route. On a clear day you will absolutely love it.

The 3rd classic trail is from First to Bachalpsee. Take the Lauterbrunnen
train down to Zweilutschinen. Get off to switch to the train going up to
Grindelwald. Once in Grindelwald, walk about 20 min further into town to get
to the cablecar station, where you take it all the way up to First. From there
walk south to Bachalpsee. There are trail signs, and it is about 45 min each
way. On a sunny day, you can get great pictures of the mountains reflected in
Bachalpsee, which is a small lake. Just Google image "Bachalpsee" and you'll
see what I mean.
Finally, if you get a foggy or misty day, you can walk further up the Lauterbrunnen valley to Trummelbach Falls, which is about an hour each way from Lauterbrunnen (or take the PostBus). Google image it to see why it is worth seeing, and the nice thing is you can actually see it just fine on a dreary and foggy day.

Awesome suggestions! Thanks!

I'll research more information about what you mentioned. I think my itinerary is starting to come together!