There are some great hostel options in Sweden and Norway if you want to sleep inside and keep costs down. Camping is the obvious other choice with being allowed camp in most places - just stay away from farmland and private property (people's back gardens!). Weather is the other factor here. Keep an eye on it and make sure you have the correct kit. Having the correct kit for the surroundings will make sure you have a good time.
It really is a brilliant area of the world to go cycle touring with the scenery being stunning around most corners. The people are friendly and great food. Good roads too.
I have not been for many years, so cannot comment on budget. Sure there must be some cost comparison websites that you can look up on google.
I myself am looking at a possible trip to Iceland. Also looks amazing too :-)
p.s. I remember the insects/bugs being a little annoying when I was there. Get yourself some repellent!