advice on travel, Munich Airport to München Hauptbahnhof, München Hauptbahnhof to Vilseck

Check connections on bahn.com - use "MUC" as starting point. This is the airport acronym; always look for your actual starting point and destination (which seems to be the airport, not Hauptbahnhof).

You have two options: Ticking "only local transport" - typically slower and less comfortable, but often cheaper than long-distance trains (especially if you want to be flexible). In this case, you will get connections that include a bus to Freising, which is not included in normal railway tickets. I assume it is included in the Bayern ticket, but maybe a local can tell you that for certain. The Bayern ticket is a day ticket for local transport in the whole state, valid from 9 am on weekdays (all day on weekends).
Or using a connection that includes long-distance trains. Not that much faster in your case. I would choose such a connection if your airline offers "Rail and Fly" tickets - these typically cost about 30 Euros or so, but are fully flexible on the day you arrive (and, I believe, the next day). You can use them to get to any destination in Germany by train.

Deselecting long distance trains and not ticking "only local transport" brings up everything that's on offer. And you can check easily that buying an expensive ICE ticket will save you but a few minutes. The cheapest way is travelling on an Bayern ticket (after 9am on workdays as chris-s says; any time on weekends) first by bus from the airport to nearby Freising, then by train to Regensburg / Schwandorf / Neukirchen(b Sulzb) and finally to Vilseck. Sometimes there are direct trains from Regensburg to Neukirchen but often you have to transfer in Schwandorf to a train bound for Nuremberg. On that route you can board any train since there are local trains only.
Buy your Bayern ticket from a ticket machine in the Airport Center or (with a surcharge of €2) at the DB ticket window.

Hi,

There is no need to change when going from MUC to Munich Hbf, the S-Bahn #8 goes directly to Hbf. ..easy

the S-Bahn #8 goes directly to Hbf

As does the S-Bahn #1, and whichever S-Bahn leaves the airport next gets to the Hbf first. Just take the next S-Bahn. They leave from the airport on opposite tracks.

But, unless you just want to see the Munich Hbf, or feel you have to ride an ICE, take the bus to Freising and the next regional train connection with a Bayern-Ticket to Vilseck. It will take a little longer, but costs far less. A full fare ticket from MUC to Vilseck will cost you 74 euro and save 40 minutes. A Bayern-Ticket, which you can buy at the airport or on the bus, costs 25 euro for one and includes any transport in the Munich metro, including the bus to Freising. (Note, you could use a Savings Fare ticket from MUC to Vilseck via ICE from Munich Hbf to Nürnberg, but it will still cost more (29,90€) and you will risk losing that ticket if the flight to Munich is late. You could always build in a couple of hour cushion to allow for a late flight, but then you would get to Vilseck later and still spend more.)