Cle7, while it might seem like a lot of connections, I took a similar route you'd need to take, from Zürich to Wengen last May on a Swiss 4-day holiday weekend. I didn't find it too difficult once we were on our journey. I compared and can see on SBB it will take 3 hours from the Zürich main station to Mürren, and our route was very similar to what you'd take, except for the final part after Lauterbrunnen. (I have been to Mürren but was coming from Geneva that time.) To Wengen, we changed trains in Bern, Interlaken, and Lauterbrunnen, and another town, but I recall each transfer felt manageable. You would also transfer at Bern, Interlaken, and Lauterbrunnen for your route to Mürren. I'll note, I was carrying my weekender backpack while pushing a 2-year old in a stroller between connections so I really feel it's manageable unless you have mobility problems. We had time to settle into our seats -- once we were past Interlaken, we had train cars to ourselves.
The area around Wengen and Mürren is spectacular -- you will encounter some slush in mid May, but we still got around okay. We were meeting friends from Basel and Geneva who normally stay in Mürren over long weekends, but they chose Wengen for an alternative this time. We took the train up to see the Jungfraujoch and the snow. Fewer restaurants in the region were open because it is not the strong tourist season, but there are restaurants open. Clouds rolled in and out but I remember a lot of blue skies. Once you want to move on to another part of the country, connections back to Bern then onto other routes or cities are fairly easy.
If you have international data (free with T-Mobile or other carriers will let you get intl. packages), keep in mind you can download the SBB app so that as you travel, you can change routes as you need should you experience any hiccups. Otherwise, before I go, I use the SBB web site to compare all my travel route options.
Rick Steves is correct that getting into nature and the mountains are the best parts of Switzerland, and should be the priority. But spending a day in Zürich at the start or end of your trip is worthwhile if you want to check it out while getting your bearings. I was warned repeatedly before I visited Zürich that it wasn't worth visiting but I found it underrated -- there are plenty of unique things to see. I agree with the comment above that suggests the boat on the lake and the Chagall windows, along with the stroll down the Bahnhofstrasse.
I hope you have a great time in Switzerland!