Sounds a great trip - definitely do it on your motorbike.
I used this route, back in 1999
Ferry to Bergen (from Newcastle I think)
Up the west coast through the fjiords, including Sognefjord as recommended by ohlala - stunning.
North Cape, then into Finnish Lapland, going south taking in the Finnish Lakes, to Helsinki.
Go to the Valamo Monastery, Russian Orthodox, guest rooms, (cheap single rooms with wonderful views) ,eat with the Russian chef and monks in the dining room, and all pretty cheap. It's on a very scenic route close to the Russian border. There you'll see how wedded to
the Finnish are. In the guest quarters, climbing the stairs, there's a bottle opener hanging on a string on every landing and half-landing, and a couple in your room!
Estonia, Poland, Austria, Hungary, Austria, Germany, ........ Calais.
On the ferry to Estonia you'll also see how serious the Finnish are about their dancing tradition!
And they're serious about saunas too of course, try out the wood-burning ones in Lapland. It's where everyone meets up. (And all speak English if necessary, but they are also very defensive, and serious, about their own language).
All on a Yamaha XT225 Serow. (I even got a parking ticket on it somewhere in the Finnish Lakes, good souvenir).
It's all you need. But I had plenty of time, 3 months for that.
I didn't take a tent and was a bit worried about the prices of rooms in Scandinavia. But I found Youth Hostels everywhere.
I left UK beginning of June to reach North Cape by the 20th, for the solstice. That's out of season and almost every hostel I stopped at was empty. Certainly, all the dorms I used were empty. And the out-of-season prices were pretty good. Most hostels are attached to large hotels and you can use all their facilities, mainly restaurants which didn't seem expensive. I remember finding the largest and certainly cheapest salmon filets I've ever encountered.
If you're going south from North Cape through Lapland in late June, that's the height of the mosquito season and you need precautions. Most people wear head-nets out-of-doors, I wished I had one, it's a good idea, you feel conspicuous without one. Lots of spray repellant needed.
The highlight for me, I'd recommend it highly, is definitely Knivskjelodden, as shown on indu's website here:
Budget travel in Norway - Minutes of a Motorcycle Addict
It's slightly further north than North Cape, so really, you've got to do it.
Start from the car park by the road to North Cape. Read the precautions (clothing, unpredictable and variable weather, detailed map, water, etc etc)
When I arrived at the North Cape gates the weather was brilliant and settled, so I decided to do this walk straightaway. Best decision of the whole trip.
I started about 9pm from the car park, arrived at the headland around midnight(!!). Most wonderful hanging sun due north over the Arctic Ocean, with just enough cloud to make massive fiery furnaces across the sky. I decided then and there, whoever wrote in the Bible about chariots going up to heaven in fireballs must definitely have been here! A big bonus was I was absolutely the only person there.
So I stayed about 3 hours, didn't really want to leave. Amazing marine bird life as well, masses of it. And they let you know, in no uncertain terms, if you scrabble too close to their nests on the rocky headland.
By the time I left it was about 3 am on the 21st, so I saw it on the solstice.
I stayed at the hostel just before you reach the gates of North Cape. That was the only time on the trip I shared a room.
Then went into the cape for the evening of the 21st. You need a big checkbook for the entry fee, and on this day it was heaving with coaches outside and tourists inside.
But the sun had gone, cloud everywhere, so absolutely no chance of seeing the midnight sun. Was I glad I took the walk the evening before!
Inside I saw an interesting aspect of human nature. I stopped for tea and chatted to the waitress.
The place was full of visitors, and there was quite a sense of displeasure, irritation and even anger everywhere.
The waitress seemed to be happy to dally a bit serving my tea.
"It's the same every year," she said (in good English). "It's all cloud everywhere, not a hope of seeing the sun, and they all take it out on us staff. They blame us for the weather! Ask us why they can't see the sun! They insist they are only here this one evening, so we should do something about it!"
I've read a few reports (including on the HUBB) where visitors have said they were dissappointed about the commercialisation of North Cape, so prepare to be dissappointed, but it's what you make of it. Knivskjelodden is the key - but you definitely need the luck of good weather!