"Should we fly and out of Stockholm? "
Since you want to see Finland and Sweden, you should fly into Helsinki and out of Stockholm (or Kiruna if you don't want to get all the way back to Stockholm from Pajala and Lulea, which I see are quite far north in Sweden). To find these kinds of flights, use the "multi city" option on Kayak, SAS, etc.
Between Helsinki and Stockholm, you can fly or take an overnight boat (almost like a cruise). For other connections between the countries, look into flying. When I flew SAS in 2003, they had a deal where you could add segments in Scandinavia to your trans-Atlantic ticket for not much money. I don't know if they still do that, but there are now budget airlines flying within Scandinavia that should make it inexpensive (one of the few inexpensive things in that region of the world).
For Stockholm and Helsinki, Rick Steves Scandinavia will have lots of useful information, including money-saving tips. You'll need to supplement with other books for your ancestral villages.