where do I start?

my great-great-grandmother Cecilia Lundgren (later to become Mrs. Charles Hilstrom in Chicago) was born in Stavanger in 1847. The family emigrated to the US in about 1853. I believe her parents names were Olaf and Johann, although I am not positive. Where might I begin looking in census, etc? Any help or suggestions would be appreciated. I know nothing more for certain than this.