Hi! Linz to Gmunden is absolutely no problem! Just get on the bus 601 (to Linz Europaplatz) at the airport. Get off at the main railway station (Hauptbahnhof) where you can easily change to a train. You can get the ticket straight away from the bus driver, just tell him "nach Gmunden über Attnang". The ticket is valid on all means of public transport, 2nd class.
In Gmunden, there is a tram waiting in front of the railway station that brings you directly to the centre, the ticket should also include this tram. (some say it's the smallest tram in the world). There are also taxis available. Have a look at http://fahrplan.oebb.at/bin/query.exe/en
From: LNZ
To: Gmunden Franz Joseph Platz ...(that's in the centre of town)
Salzburg, St. Wolfgang and Bad Ischl sounds good. I can also recommend you Hallstatt, which is a small village between steep mountains and lake Hallstatt. If you go there, don't forget to visit the "Gebeinhaus" next to the catholic church (the one higher than the evangelic)... Have a look at www.tiscover.at/hallstatt (English version link on top).
If you want to go there by public transport, I'd recommend you to go by train from Gmunden to Hallstatt (you should get a ticket for this from the tram driver, if not, get it at the rail station.) If rail stations don't have a ticket window or a self-service machine, you can get tickets from the conductor (and for a small fee also if you don't have time to buy tickets before). From Hallstatt rail station to the village, you have to cross lake Hallstatt on a boat which leaves some minutes after the train has arrived. Single fare of the ship is € 1,90, mind that the last ship leaves Hallstatt at 17.50. If you don't want to go by ship, there's also a bus service available, just enter the details in the timetable link...
Hallstatt also has a salt mine... tiscover.at/at/…intern.html
Hope that I could help you a little bit!