Do you recommend getting a bus or train from Milan's airport to get to Milan's Stazione Termini?
Also, can I buy a train ticket at Milan's Stazione Termini to get to Venice, or do I need to do that in advance?
Fast trains like the one from Milan to Venice are cheaper to buy the earlier you get them which many discount options if you get in early. The problem is that cheaper fares are less flexible and/or non-refundable so you need to buy far enough in advance to allow for flight delays or other issues if you buy in advance. So unless you're really sensitive to pricing I'd just wait and buy the next available ticket even if it is at full price.
Trenitalia has an app I'd recommend you download and use while in Italy. It allows you to get schedules, buy tickets and validate tickets and track trains in real time.
Check .Italo also for fast trains between large cities.
It's been a while since I've been through Milan but if the train station is your destination I would take the train in and you can buy tickets after you clear immigration. If anything has changed I'm sure someone will speak up.
Have a great trip!
=Tod
If you want the main train station, it's Milano Centrale. (Termini is the main station in Rome). Take the train. For Venice, you would want either a high-speed Freccia train run by Trenitalia, or by Italo. You can buy your ticket at the station at the regular price. Or you can buy a discounted ticket in advance. But those come with restrictions, and generally aren't recommended if travelling after arriving from a flight (due to possible delays during the flight or at the airport which might cause you to miss your train).
Termini is a station at Rome. I think you mean Milano Centrale. That is where the trains to Venice originate. You can buy the ticket there if you like. Buying in advance can save money, but that is difficult to plan if your are arriving in Milan by plane
Station names:
Milano Centrale
Venezia S Lucia
https://www.trenitalia.com/content/tcom/en.html
The Malpensa Express is the train from MXP to Centrale
Takes about an hour, runs about every 30
min
Run by Trenitalia
Edit
Typo corrected
Actually every 30 minutes at 13 and 43 past the hour from Terminal 1. Make sure you get on the train going to Centrale, as there also trains at 26 and 56 past the hour going to Milano Cadorna, the wrong station to get to Venice.
Many thanks everyone for your help.