Milan Hotel recommendations and transfer to Switzerland

[HIS LM]

Flying to Milan in October for Wedding anniversary, the plan is to explore the sites in Milan for a few days (suggestions please) and then pick up the Bernina Red Train from Fermata Milano Centrale.

Looking for Hotel recommendations in Milan around £250 per night and best booking web site.

After that excursion we will travel from Milan to Saas-Fee in Switzerland for 3 nights, again looking for travel options for the route from Milan to Saas-Fee and back to Milan.

Advice please.