Factoring in cost and scenic route, what is the best option for travel between Luzern/Lucerne and Milan?
Go to www.sbb.ch/en. Put in Luzern to Milano Central, the in the "via" box, enter Goeschenen. That will take you mostly over the Alps through the old Gotthard Tunnel. Similar to the Gotthard Panorama Express, but skips the boat ride portion.
Why would we want to skip the boat ride? Cost? Less scenic?
Is there a way to go from Luzern to Milan going on the Bernini Express (which is reported to be an exceptional experience)?
Bernini Express is quite out of the way (it goes through eastern Switzerland and then south). On the Gotthard Panorama Express Lucerne-Lugano is 150CHF in first class, per person and 127CHF in second class, per person. Plus a Panorama express surcharge per person of 16 CHF, and the seat reservation charge...
Very scenic, amazing train tunnels. Lugano on to Milan is extra.
Sam is right - check out the sbb.ch/en website for all of the options.
Because you asked about a low price scenic route from Luzern to Milan. You have to go back to Zurich then to Chur to get to the Bernina Express. And that is more money.
My trip was a little different from yours, but maybe there is something here that helps you: We recently did a similar route as the Gotthard Express -- took the boat to Brunnen instead of the very end of the lake, and from there took trains to Locarno. Our hotels in Ticino all included the Ticino card, which was free bus and train in the region (we stayed in both Locarno and Lugano--loved both, they're very different). Although we had to change trains, it was easy and painless. When we left Lugano, the train was included in the Ticino card to the border, and then about 4 Euros each to Como, where we got a ferry to Bellagio. The boat ride was spectacular, and I don't think it cost any more than the train.
We did this mid-week, mid-day, but I've been warned that the trains going from the top of Switzerland down to Ticino get very crowded on weekends.