I was fortunate that my mother has been into genealogy. She had me filling out a pedigree chart when I was eight. She has one branch of the family traced back to the 1200's in England. Which is NOT easy - no such thing as a census. The only records are in churches - births, baptisms, weddings, funerals, etc. And there have been so many wars big and small in Europe that a lot of records got destroyed.
One of the things I like about genealogy is the stories. Not just the name, date, and place, but the why. Being from the U.S. the question was always why did that person come to the U.S? What was the thing that tipped the scale? Why was I born here, instead of in Malmo, Sweden where my great-great-grandfather (after whom I am named) lived before he came to the U.S. and settled in St. Louis? I know in another branch of the family a son was disowned in Wales (it was a religion thing - the son joined a different church), and he came to America.
Don't know for certain where this will lead you. If it leads back to Sweden, one of the biggest challenges in genealogy in the Scandinavian countries was the "last" name changing every generation. Just to pick some names out of the hat, you can have Anders Petersson, and his father was Peter Bengtsson, whose father was Bengt Andersson, and so forth.
One resource I haven't seen mentioned is the LDS church - commonly referred to as the Mormons. They have more records than anyone. If there is a local branch near where you are, a polite request for help may prove beneficial. When I was a teenager there was a satellite library at the branch in the town where we lived, and mom spent every Tuesday there, looking at microfiche and ordering other available records.
Good luck in your search. Like I said, after you find the who, when and where, the next thing you will want to know is the why.