Train help

Generally a ticket to a train is sold by the national company at the begining and end of the journey. So check both for prices they do vary from one company to the next for the same seat on the same train. Now for this trip, if all the OBB prices were within a few Euros of being the cheapest, I would be tempted to buy them all from OBB just for convenience. But there is a real possibility that the Budapest ticket will be 20 euro or more cheaper on MAV.

What I would do:

Füssen to Innsbruck Austria
Check prices and schedule on DB and OBB
Innsbruck to Salzburg
Salzburg to Vienna
Check prices and schedules on OBB
Vienna to Budapest
Check prices and schedules on MAV and OBB

DB https://int.bahn.de/en
OBB https://shop.oebbtickets.at/en/ticket
MAV https://jegy.mav.hu/

Download the phone app for the national train companies that you end up using. Load the tickets on the app and use that on the train. Just easier.

Munich to Fuessen is a regional train. No reserved seats possible.

The quickest way (and cheapest) from Fuessen to Innsbruck is a bus to Pflach, Austria, then a train to Garmisch-Partenkirchen, then a train to Innsbruck. Train cost is 85 EUR for 4, again, no seat reservations possible. As an alternative, take a taxi to Musau Uhlrichsbruecke (just before Pflach) and get the train there. That is about a 3 mile taxi ride, so with 4 people, would not be too much per person.

The rest go to www.oebb.at/en to get tickets. Seat reservations are always extra, about 5 EUR per person.

4 adults. Reserved seats

Not a problem where reserved seats are offered. See the other posts for trains with open seating only. The OBB charge for a seat in any class is 3 euro. MAV I belive charges 2 euro, but I could be wrong on that. But if not 2, then its the same as OBB. It does depend on when you book and when OBB runs out of their discount tickets, but MAV could potentially save your 20, 30 or more euros per ticket x 4 traveling is real money. Same train, same service, same everything.

Booking too far out really acheives nothing but 3 to 6 weeks isnt a bad idea to be sure you get a discount ticket and a four seats together. Still, since you are planning, check the schedules odds are they wont change between now and November and check prices for budgeting. Then October do the buying.

Oh, forgot. RegioJet. Not sure how many of these routes the private company does. I know they do Vienna to Budpaest and they will be the least expensive. Only drawback is the train goes to a station sort of on the fringe of town (not a very pretty station at that) and you will spend some time on a metro or a tram to get into the city center. https://regiojet.com/

Then there is another private company WestBahn that serves Austria and Germany. I know nothing about them. https://westbahn.at/en/ or which routes they do.

AND

Using Daytrip.com Munich to Fussen on one day and Fussen to Innsburck on another day is about 550 euro for the four of you in a private van. Or Munich straight to Innsburck is about 350 euro. And they have some interesting stops along the way that you can buy for fairly reasonable prices. Really not a bad service. I've used them a few times.

Munich to Fuessen by train costs 62 EUR total for all of you with a Bayern Ticket, as long as you leave after 9 am on week days, or anytime weekends.

I am finding train travel a little daunting!

You can also travel by bus, e. g. Flixbus.

Westbahn competes with the Austrian railways to destinations westward from Vienna. Initially it was just to Salzburg but now a few trains run to Innsbruck or Munich. Compare the prices and departure times, it may be cheaper with them if you book in advance.