If you are looking for information about families who immigrated to the United States from other countries, naturalization records are very helpful. This is one of the few pieces of information that may pin down the date of arrival in the United States, the port of arrival, and possibly the port of departure. The forms changed over the years and different information was collected at different times. If you are interested in locating passenger's manifests, the port and date of arrival are critical pieces of information.
Generally you will find two sets of naturalization papers. The first was filed relatively soon after arrival and is a declaration of intent to become a citizen. The second set was filed after the applicant had fulfilled a subscribed number of years in the United States and has a citizen vouch for his good character.
If you are not sure that searching for a naturalization record is the next best option for your research, consider using the advice feature of this site. This will help you pick your next best steps in your research. Go to Genealogy Search Advice.