Ancestry Library Edition is the best starting point for your research. Ancestry combines hundreds of databases of US census, passenger list, church, military, vital (birth, marriage & death), court, immigration, and naturalization records, as well as record collections from Canada, Europe and Australia. Here are a few examples of potentially helpful types of databases in Ancestry. NOTE: databases may be searched separately or all-at-once.
FamilySearch, a service of the The Church of Jesus Christ of Latter-day Saints. You will be asked to create a free account.
Use the "browse all collections" link to drill down into specific segments of the site. Some potentially useful databases in Family Search include:
Heritage Quest Online (available from the Chicago Public Library; apply for a borrower's card). A good complement to Ancestry for the census; Heritage Quest also has tens of thousands of compiled family genealogies accessible in full text.
The US National Archives (NARA) maintains a number of useful tools for researching family history, for example:
This is a selective list of free genealogical sites that provide access to both discussion lists and original documents.