Make sure that you understand the distances involved when visiting Norway -and the cost of long distance transport.
Then try to get some IDEA of the region you are interested in!!! - with the knowledge you have, a guidebook form the local library, and homepages like www.visitnorway.com www.visitoslo.com - and the homepages of the tourist office of each town you are interested in,
It is really a waste of time if ppl. start to give all kind of info on the extreme north, Svalbard, Lofoten, trondheim, whale watching, raindeers...if you from the beginning are sure that you will "do" the usual 2 days Oslo, Norway in a Nutshell trip to Bergen an maybe trying to visit one more fjord. This will easily use up your week.
A good trip round Norway for the major must sees is a month+ project
Cannot advise on car or public transport until you have made up your mind re where to go. You cannot travel from one end of Norway to the other (and seeing anything) by car in one week.
The Hostel question one below here (if you do not chose a specific Scandinavian country) has been answered 3 below here.