I read Lucas's comments about Wengen and Lauterbrunnen to be neutral, and I personally would recommend Wengen. I like the views better.
The cliffs around Lauterbrunnen are far enough apart, and the valley beautiful enough, that you would not feel claustrophobic.
In mid-May, the Valley floor would be mostly free of snow. The waterfalls will be at there best, working hard to drain snow melt. There could be residual snow around Wengen, or you might get lucky with the snowpack from the Winter, and have it all melted by then.
The wonderful easy trail from Männlichen ( well up above Wengen) will not be hikable. Blocked with snow or danger of snowslides until mid-June, usually.
As the altitude increases, you get more and more into the remnants of Winter.
Around Luzern and Bern, Spring will be well started.
Both have really nice old towns.
In most areas, there will be more to do than you have time for. So, reading and planning as you are doing is a good way to try to figure out ahead of time what you will focus on. The itinerary looks good, Lucas suggestions make sense to me, too.
I have attached a few random relevant pictures.
Since you are already in Europe before you arrive in Basel, you won't have to deal with jet-lag on your first day.
Basel, Luzern and Bern are all close to each other by train,by the way. The fastest trains run about an hour or less, and there are frequent trains.
The timetable will be valuable for you, and the SBBoffers a smartphone app, useful on the road. I like a bigger screen for planning.
Read the into page carefully; it is very helpful.
Departure from Geneva could be easier than from Zürich, if your last night is in Montreux. It is closer. Zürich has a lot more choices of international or intercontinental service. It is about 1 1/2 to 2 hours longer on the train, however.