Train Tickets: When to buy?

As those are "international" tickets ( crossing a border) you can get substantial discounts by buying 3-4 months I would start looking now.

Check Trenitalia as well as OeBB for the Innsbruck to Bolzano leg. It might even be available from Bahn.de if the train originates in Germany.

Bolzano to Munich I would definitely buy on bahn.de. We did this several years ago and the discount for advance purchase was more than 50%.

Every ticket I have purchased online from those three companies came as a "print at home" PDF attachment to an email. It has never been an issue. The "print at home" option should be clear to you during the purchase process.

Some US credit cards may not be accepted, and you may have to notify your credit card issuer first. I use an AmEx card with no problem, but occasionally they will text me to ask if it is I attempting the purchase. Once I confirm, it goes right through.

There's an express train from Bolzano to Munich non-stop...that's great.

It is not nonstop, but it is direct. The EC train makes 9 stops between Bolzano and Munich Hbf.

The advantage to buying ahead is that you get a discount for a nonrefundable ticket. I am looking at the DB website for May 21, I see the 10:34 and 12:34 trains available for 29.90 EUR, and the 14:34 and 16:34 trains for 24.90 EUR. Bought at the station they are all 66 EUR.

When you buy on-line, you get and email with a pdf print at home ticket. Or you can down load heir app and have he ticket on your smartphone.

I checked Bahn.de

For Bolzano to Munich, a Super Sparpreis ticket bought today for travel tomorrow would cost €54,90. A Super Sparpreis ticket bought today fromtravel May 4 would be €29,90. These are inflexible tickets ( can't be changed) so keepmthat in mind.

They will also sell you the ticket from Innsbruck to Bolzano onnthe direct train coming from Munich. For 4 May the discount offer price is €19,90. But you can get a regular ( flexible) ticket for €10 more so maybe that is worth it.

And if you are traveling as a family with children,there may be other prices and discounts available.

In any case, I recommend using Bahn.de for both purchases, as it is easier to navigate than OeBB, in my experience.

Will I download them?
will they email them to me?
Will I print them?

Yes to all 3 questions.
The ticket comes as a PDF file, either downloaded when you buy and/or e-mailed to you (be sure you enter your e-mail address correctly).
You print it out and bring it with you to show to the ticket checker on the train. It is checked once the train is under way, not before you board.
The ticket will give train details (date, time, from, to train ID), and list your seat numbers.
You may only get 1 ticket for everybody, it will list all the seat numbers. You may get separate tickets and reservations.

There is a screenshot of a self-print ticket here: https://accesrail.com/wp-content/uploads/2015/12/OBB_travel_document.png
And some examples of reservation vouchers here: https://www.academia.edu/40295552/OEBBTicket

Online payments in the EU require a two-factor authentication, i.e. the credit card data alone is not enough. Your credit card may not be enabled for this - contact your card issuer.

Amex may be an exception by not supporting European security levels.

My Australian issued MasterCard works on these sites. When I get to the purchase option after entering card details I get a message that it is redirecting me to my bank and then a code is sent by my bank to my smartphone by SMS. I just then put that code in when prompted. Easy.

I also always save my PDF tickets to my iPad (which comes on our trips) as well as printing them. If they have a QR code the ticket inspector just scans this (either from paper ticket or device). I have never had any problems on two 5 week European trips where we travelled exclusively by train.

When I get to the purchase option after entering card details I get a message that it is redirecting me to my bank and then a code is sent by my bank to my smartphone by SMS. I just then put that code in when prompted. Easy.

That is what I meant when referring to two-factor authentication required. Most Americans do not consider this as easy, though.