If you have an interest in genealogy, the library is one of your first stops. Visit the Genealogy page on the website. There are two online databases available free through the library: Heritage Quest and Ancestry. Ancestry is only available at the library, but Heritage Quest is accessible from any computer anywhere with your library card and pin number. (If you don't know your pin number, go to the checkout desk.)
These databases change constantly, with new information and resources added. Ancestry is the larger database, with huge amounts of information including census records, state birth, marriage and death records, tax records, immigration lists, military records from most wars, and much more. One option to try,if other options are exhausted or fail,is going to the alphabetical listing of databases and scanning through the list for potential sources.
For instance, if there is no record for an ancestor from Michigan, you could check the county directories or the cemetery records for that county by going to the M's, then to the Mi's, finally finding the section on Michigan and that county's listings within the Michigan section.
A recent check for my ancestors yielded many results where previous efforts had been fruitless. It was exciting to find military records for my father and grandfather, tax records from the 1700's for a great great great grandfather, Revolutionary War records for a even older grandfather. None had been found on previous searches.
Heritage Quest also features the census records, as well as searching more than 24,000 historical books, 2 million articles, the Freedman's Bank, Revolutionary War records, and other sources. Another resource that is available is the General Land Office records, from the Bureau of Land Management, at http://www.glorecords.blm.gov. This is the only record I have found to date for a forefather who lived in Georgia.
It is best to start any search with precise information--first and last names, birth dates, and place of birth. If any of this is missing, you might go to the more recent ancestor to seek the information you need, and then try the older one again, once you have more detail.
For Jackson ancestors, the Carnegie Library has newspapers on microfilm, including the Jackson Citizen-Patriot, back to the 1800's. There are also print records for county cemeteries, directories, and more. These materials are available in the reference room or in the Minter VanOrman History Room.