If you want to reach Murau - or any of the nearby villages - by rail, then you'll have to take the narrow gauge railway - the Murtalbahn. The Murtalbahn travels between Unzmarkt and Tamsweg (in Salzburgerland) and there are trains usually every other hour. The service usually runs about once every two hours, although there is a bus service usually running along the same hour route between these times. The trip is worth down - there is glorious countryside to take in with mountains and the pretty Mur valley. For people with bikes you are best checking in advance about space for bikes - it is a very popular cycling route. Unzmarkt has mainline trains heading towards Vienna and Klagenfurt/Villach.
Skiing and snowboarding in Austria is unmatched. Murau has 2 or 3 slopes nearby. We went to the Frauenalpe which wasn't large but was definitely lots of fun. This same mountain would make a great hiking spot in the summer months.
Equipment: Bring your ski clothing. You can rent the skiis there.