Flew to lapland (Swedish side though) last year.
Dublin --> Stockholm with Aer Lingus
Stockholm --> Kiruna (return from Lulea) with I think Norwegian or somesuch.
all in all less than 350 per person return. Was happy enough with that.
Not sure how I would tackle Finland. Potentially Ryanair to Tampere and than again Norwegian to go further. Stockholm however seems to be a good hub for going further North, as was Oslo.