If you are staying in one of the hotels near the north cemetery (Nord Friedhof), the Lufthansa bus is the way to get there. It goes direct from the airport in about 20 minutes, costs less, and has no changes. However, staying there is problematic if you want to go the city center, Marienplatz (8 minutes, 3,50€/P on the U-Bahn), and even more difficult to get to a train to Salzburg in the morning (almost 20 minutes, one change, also 3,50€, but included if you are using a Bayern-Ticket).
If you want to stay very close to the north side of the Hbf, it's almost a toss-up - a little less for the bus, about the same amount of time assuming no traffic, and 2 S-Bahn every twenty minutes vs 1 bus.
Any distance from the Hbf to your hotel - go by S-Bahn. The MVV fare is a little more (12,30€ for a single ticket vs 11,50€ if you buy your ticket from the driver, but the MVV fare will cover you not only to the Hbf, but to anywhere in the central district of Munich (S-Bahn to the Hbf, Marienplatz, or Ostbhf, then U-bahn, tram, or bus to your ultimate destination).
And if you purchase a single Tageskarte, at 13,70, or a Gruppen Tageskarte, for 25,70 for 2 to 5 people (12,85€ for 2), you can use the ticket to travel to anywhere and back in the central area for the rest of the day.
No, if it were up to me, I'd stay near the Ostbhf. If I thought I'd feel up to going into Marienplatz that night, I'd get the Tagesticket and take the S-bahn after I checked in. Then, in the morning, I'd be right there at Ostbhf to catch to RE to Salzburg in the morning using a Bayern-Ticket.
Actually, if I were within walking distance of the Ostbhf,I would use a BOB Guten-Tag-Ticket. It's the same as the Bayern-Ticket, but without use of the local, MVV, transport to get to the regional train, and costs 23€ for the first person, 8€ for addition riders, 31€ for two.