You have two posts going on this topic: I will reply on this one and refer to it on the other one.
We like to fly into Zurich to get to Italy. It is a good way to incorporate the scenic Bernina Pass route into a trip. The Bernina Pass is the most scenic of all the so-called scenic trains in Switzerland, and the only route that goes over the Alps instead of under them in a tunnel (although the tunnel on the old Gotthard Pass route is quite short).
You can take the named Bernina Express train with panoramic cars or a regular regional train on the same tracks, which is less expensive.
From the Zurich airport, travel to the m;win station and transfer there to a train going to Chur. Depending on the time of arrival of your flight, you could overnight there, but it is better to continue to the Engadine area, stopping in either Samedan or Pontresina. The latter is 3 hours 18 minutes from Zurich.
Another option would be to go straight to Luzern from the airport for your first night or two. You would then return to Zurich to travel to Pontresina, adding an hour to that journey but it won’t be after a long flight!
Spend 1-2 nights in your Engadine village, then travel over the Bernina Pass to the Swiss/Italy border at Tirano. There you will change to an Italian regional train to go to Varenna on Lake Como. Spend 2 nights there. Then travel one hour to Milan and change to an Intercity train heading to the Cinque Terre area. There are two routes you can take; one via Florence and one along the coast via Genoa; we like the latter. There is a noon-ish Intercity train leaving Milano Centrale that goes all the way to Monterosso al Mare with no change at Genoa.
For the return to Zurich after your Florence stay, the fastest route it Florence to Milan to Zurich. There is a direct train (under the alps) from Milan to Zurich that takes less than 4 hours. Buy tickets around 3 months advance on Trenitalia to get a “mini” fare as low as 19,90 euros on this train.
I like to use Bahn.de, the German train website, for route planning as it is the most user-friendly. But you will have to buy your tickets on the Swiss and Italian sites, SBB.ch and Trenitalia.