Nice to see that you´re intrested in coming into Finland. Rental cars are very expensive as is gas. Forget that option, unless you have loads of cash. Taking a bus to Rovaniemi in Finnish Lapland should be doable. From there you can take another bus, or take the train or fly straight to HEL. One-way flights start at 39€ all in from
www.blue1.com I recommend doing that as on the train and bus you´ll mostly see forests and some more forest. Plus it costs at least the same as flying if you plan ahead.
I´ve never been that far north as you plan on going. But definitely it should be intresting. Are you going in the summer or winter? They only have two seasons over there.

Summer means endless days with no sunset for over a month. Winter means very cold with the sun not rising for over a month. Both are intresting as extremes. You should post under the Scandinavia forum and read some posts on the SAS forum too. That´s where most people from Norway and Finland post.
p.s. Feel free to PM me if you need any tips to Southern Finland and Helsinki. I´m always willing to help and meet other FTs.