This sounds similar to my itinerary this summer...Denmark and Norway for two weeks...but we're not rending a car, just public transportation. We're starting off in Copenhagen and then ending our trip in Bergen. (We decided to do 4 days in Copenhagen and only 2 days in Oslo because there were more things in Copenhagen that we wanted to do.)
Start off in Copenhagen (enjoy the city, but maybe take a daytrip somewhere, perhaps to Roskilde, if you're interested in seeing their Viking Ship museum or Helsinore looks nice too)
Overnight ferry from Copenhagen to Oslo will save you some daytime (leaves Cop at about 4:30 in the afternoon and arrives in the morning in Oslo). I've researched the ferry and it looks pretty nice.
Oslo -- folks museum, Viking ship museum, Vigeland Park with sculptures and a museum
Oslo to Bergen via "Norway in a Nutshell" (you could stay overnight somewhere, perhaps Flam, if you want to do this slowly and not do NIN all in one day). We're taking NIN slow and doing it ourselves and there's lots of threads on this forum with good advice about NIN. I've learned a lot from others on here. We decided to stay in Flam, but if you're staying in Flam then I would recommend that you try to book a room soon because we had difficulty finding a "cheaper" option for July. We're actually going to stay at the hostel there. We chose Flam for 2 reasons...it is along the NIN route and it looks beautiful. I hear there are some nice trails in and around this little town too and we like to do moderate hiking trails. You can book all the trains, boat, and bus yourself. For NIN, it's 2 trains to Flam (Oslo to Myrdal then Myrdal to Flam). From Flam, you can take the scenic boat ride to Gudvangen, then the bus from Gudvangen to Voss and a train from Voss to Bergen. I believe the website for booking trains is nsb.no (we haven't booked yet) and I've heard that US credit cards have been a problem for some when booking train tickets online so you can call and book them over the phone too. I've also heard that the train from Oslo to Myrdal can sell out, so we're booking that one ahead and you can book it up to 3 months ahead. I'm sure all the trains are scenic, but the highly recommended train ride is from Myrdal to Flam. Visitflam.com has info about the boat option. The popular boat route is Flam to Gudvangen, along the Naerofjord and this fjord looks unique and beautiful because it is so narrow.
Have a fun trip!