Travel from Munich to Innsbruck by train.

The cheapest and fastest way is using an RJ or EC with a pre-booked OeBB "Deutschland Spezial" - ticket (prices start at €14). Book at the OeBB web site and use the print home option. If you have more time you could go instead the scenic route over the mountains to Mittenwald and Garmisch. A DB ticket "Werdenfels+Innsbruck" is the cheapest ticket for that route. You can buy it from any OeBB ticket machine at the Innsruck station.

What do you mean by best - lowest cost? Fastest? If you can commit to a specific train (date and time), you can save money by booking in advance, but the ticket will only be valid on that train, so you risk losing the cost of the ticket if you miss that train.

I think the fastest train would be one of the EuroCity (EC) that goes from Munich to Innsbruck about 5 times per day and makes the trip in about 1 hour 45 minutes without changes. Advance purchase price can be as low as 19,90€.

The RailJet (RJ) leg is from Kufstein to Innsbruck. You also need to use a Meridian regional train from Munich to Kufstein.

I agree with SLA that the Mittenwald route would be more scenic, although take longer and cost more, at least for a single person.

Thank you, very helpful.