Travelling around. The things you need to know

Norway is a beautiful country to see, but it is also not very densely populated and there can be great distances between cities and nature so there can be a lot of moving arround involved.
Usually plain tickets are quite cheap but when it comes to bus or train, it can get very expensive. You can also come to Norway by personal car with a ferry, but there are things to take into consideration. Any technical help in Norway is expensive,  so you need to have a great insurance but also be very sure that your car is up to technical challenge of driving in different terrains specially winter which is october in the more mountainess areas.
Which is why my suggestion is that you get here by a plane and rent a car. It is not as expensive as going arround with a public transport if you are more than one person and  it is much safer than going with your own car as these companies usually have better local ensurance and cover service expenses. There is also a considerable amount of electrical wehicles avaliable for rent but I would not advise them other than getting around the city because  mountains are a challange for them . As I hears from my freinds, the car lost about 20% charge by just going up the hill . So they are a good option in the city but not in the country side. If youare more fitness driven you can travel by bike. There are great routes around country and people are very tolerant torwards cycling.
The other thing is where to stay . Hotels in Norway are fabulous but also can cost a bit.  Another thing is that if you are not opting for McDonald's eating at restaurants can also be quite costly. That is why  if you are not staying in the city I suggest  mountain cabins called Hytta in Norwegian. They are usually cheaper than hotels and can accommodate more people, and they have a kitchen so you can cook for yourself.  You can book one through official sites like booking.com or others but I  suggest trying airbnb this time. Norwegians usually own a cabin themselves so you can get one for a cheaper price and better equipped. a cabin can usually cost from 50 to 100 euros and can usually accommodate 4-7 people. It depends.  If you stay in the city that can get tricky. But there are options. I recommend a Scandic hotels- they are great and have a wonderful breakfast option which can save you some money . It is also a bit cheaper to book it from their website . They have great location usually in more than one location in the city. Other than that a hotel room in Oslo for example will be about 100 euros for night, depending on where you are staying. Yet again Airbnb vil probably have cheaper options. 
If you ask me I suggest you start in one city , check it out for one or two days and then rent a car and drive up to another city, soaking up as much nature as possible. For example from Oslo to Bergen or Oslo to Ålesund. Rent cabins for an authentic Norwegian experience and also to save a bit of money.