Train tickets

I would buy trains that go directly from Milan to Venice as soon as they go on sale. The direct trains on this route are known as Frecciarosa and come with a seat assignment. You can search and buy these at trenitalia.com 90 days in advance. Milan to Varenna you can buy those when you get there as those are short distance trains known in Italian as regionale. The price is fixed on regionale trains and no reservations are needed.

this site may help wth your train questions, was great for me. https://www.seat61.com/Italy-trains.htm

Betty,
Are you planning to travel to Venice upon arriving to Milan?
If you’ll be flying into Milan, it’s generally not recommended to book your train tickets in advance due to possible unforeseen delays ( plane, passport control, baggage claim, etc...)

You can, however, book your tickets from Venice to Milan, as soon as possible to take advantage of discounted tickets (usually available 120 days in advance)
High speed trains (freccia) are very comfortable. I usually book 2nd class.

When traveling from Milan to Varenna, you’ll take a Regional train. You can buy these tickets at the Malpensa airport ( upon arrival) or at Milano Centrale station.

You can check train schedules on Trenitalia.com and you’ll need the train stations in Italian as follows:

• Milan = Milano Centrale
• Venice = Venezia S. Lucia
• Varenna = Varenna-Esino

Make sure you buy round trip tickets, from Milan to Varenna, as the tiny station in Varenna is unmanned and the ticket machine may not be working.

Don’t forget to validate (date/time stamp) your Regionale train tickets prior to boarding the train to avoid hefty fines.

Freccia tickets (Milan to Venice) do not need to be validated because they are train and date/time specific.

Enjoy your trip!

these at trenitalia.com 90 days in advance

Between 120 and 180 days in advance, to be Accurate. 90 days in advance some of the cheapest fares could be sold out.
Even if regional trains can't sell out, there are reasons to get tickets in advance online: Online purchased tickets do not need to be time-stamped before getting on the trains.

Both the tobacconist shop on Varenna's main street and the travel agency near the train station sell Regionale tickets, but there is internet in the Lakes District.

Thanks to everyone who replied to my train ticket post! Very helpful information!

Italo also runs high-speed trains between Milan and Venice, although probably fewer per day than Trenitalia. Sometimes their prices are lower and/or discounted tickets are available after Trenitalia's discounted tickets have sold out. Second class tickets are perfectly fine. No need to consider a higher class of service unless they're offering a price equivalent to second class.