You can explore your transportation options on the SBB website.
All your trips will involve train for at least part of the way. Depending on exactly where you are going, you may need to augment the train with a postbus or some sort of high-mountain transportation. The SBB website will put the entire trip together for you.
It's generally recommended not to stay in Interlaken, which is down in the valley, but rather actually up in the mountains above it. Wengen is very popular, but there are other options.
Caumasee is a lake, so you'll need to do a bit of research on exactly where you want to go--to the town of Flims or somewhere else in the area. In any case, it is best approached from Zurich. If you travel from Lucerne to Caumasee, the detault routing will be through Zurich. Since you also plan to go to St. Moritz, I think Caumasee is best positioned between St. Moritz and Zurich in your itinerary.
Your stay in Switzerland is long enough that you will likely benefit from one of the Swiss travel cards/passes, so check out the "Travelcards & ickets" link near the top of the SBB website. To make the best choice you'll need to research the full-fare ("No Reduction") cost of each trip you plan to take and be aware that the various cards/passes offer different advantages on some of the high-mountain transportation.