Flying into Milan

No, you don’t have to.

You can just buy the ticket after you arrive. It’s handy to have the Trenitalia app, so you can buy it without standing in a line or trying to use a ticket machine.

That’s a very convenient hotel to the train station.

I normally just buy tickets for Regionale trains from one of the automated kiosks at the station. They have an English language menu and are very easy to use. However one important point..... if you buy paper tickets from a kiosk, they must be validated (time & date stamp) using one of the machines in the station prior to boarding the train. This short video will explain how to do that - https://www.youtube.com/watch?v=sxJBtMdJf30 .

You will not be disappointed using the train. I’ve used it from the airport to Centrale Station more than once. On my day of travel last year it was on time. It was clean, well suited for passengers with luggage. The ride was very smooth. Additionally the station at the airport is very nicely maintained and staffed. Although I used the app to purchase my ticket (immediately upon landing in Milan) I had the occasion to speak with staff because I had purchased a ticket for a later train. It had taken much less time to locate the train station than I had projected. They informed me that my particular ticket permitted me to board an earlier train if desired which I promptly did. If you choose to use a paper ticket do not forget to validate it.

I think Milano Centrale has tap and pay for the train to the airport.