Visiting Switzerland close to the Italian boarder

"My tour will start in Lake Como after my week in Switzerland" Where exactly on Lake Como (it is a big lake)?
You also don't want to duplicate anywhere you will see on your tour, where is the tour stopping before and after Luzern?
If it is Como town, that is a short train ride from Lugano. If it is somewhere else on (not in ☺) the lake, you may need to amend.

As you are starting in Milan, taking the Glacier Express route to St Moritz is a good fit. You should overnight in Milan, you don't want to do this the same day you fly in (train from the airport into Milan). Next day, train from Milano Centrale station to Tirano. Then change to the train for St Moritz, over the Bernina Pass. Overnight in St Moritz, or, if you have time and appetite for more mountains, continue to Chur and overnight there.
There is a daily bus from St Moritz to Lugano, which allows you to have 1-2 nights there. Then frequent tains from Lugano back to Milan (if that is where you need to be).
Another option is St Moritz (train) Thusis (bus) Bellinzona (train) Lugano, which gives you another route over the Alps by bus this time. Bellinzona is alos worth a stop, three UNESCO World Heritage castles.

Train and bus times for Switzerland on the SBB website: https://www.sbb.ch/en/

It probably wouldn't fit in with your other plans, but the Centovalli rail trip between Locarno (Switzerland) and Domodossala (Italy) is very nice.

We were advised not to stay in St-Moritz and were so glad we followed that advice. Pontresina is close and there is a small train that connects Pontresina to St-Moritz. Pontresina is charming with beautiful painted houses. Look at Hotel Collina.

Agree with Suki's post. Pontresina or nearby Samedan will offer less expensive lodging and less glitz than St. Moritz. They are all very close to one another and when you get to Pontresina ( which you will reach first) you will have crossed the Bernina Pass and enjoyed the best of the scenery.

Lugano is a nice contrast to the rest of Switzerland: Italian speaking and Italian food dominate. Very pretty location on a lake, but maybe too repetitive if you are also visiting Lago di Como.

We were warned that St-Moritz itself is not attractive, lots of concrete buildings which we found to be true.

I am skeptical of the link the above new poster set. I did not click it but googled. It appears to an online casino website.