"I find transport in Swiss very confusing with all trains, buses, cogwheels, gondolas n boats."
Before you go there, you're right, it is confusing - all those unfamiliar Swiss-German place names, and the need to keep changing modes of transportation. But when you actually are there, I promise it's easy. Unless they've blasted a tunnel, transit can't go through mountains - only up, down, or around them. So, to get from Luzern to Rigi, you take a boat on the lake, then a train or cable car up the mountain. You can't get lost when you can actually see it in 3-D. Plus, there's lots of people around to ask for help, and just about everyone will speak enough English for the task.
One thing to be aware of: You can ascend to Rigi from either Weggis or Vitznau (on the same boat from Luzern). At Vitznau, it's a short and only slightly inclined walk from the boat dock to the train. But at Weggis, it's a VERY steep uphill climb to the cable car. I walked it downhill (from the cable car to the boat dock) and it took me 10 minutes; it would have taken at least twice as long and been quite unpleasant if I had tried it in the reverse direction. So, if you have any mobility impairment, knee problem, etc, go up and down via Vitznau, not Weggis.
I went to Rigi because it was fully covered on my Swiss Travel Pass, while Pilatus and Titlis would have been only partly covered. I enjoyed it very much, but can't compare it to the other two.
I do agree that you should check webcams before any mountain excursion, and to help you decide which one to do. There's no point in going if the top is solid white out, particularly if another excursion option has better visibility.