While my dad was still alive he and I did some genealogical research. We spent a lot of time in libraries in the towns where we knew that people in the family were born and died (this was in 1997, at the time not as much was available online as there is now). I am still missing definitive information about a single generation from the Revolutionary War period, but otherwise I have everything back to Sarah Chilton's arrival on the Mayflower
The best place to start is with family members who are still alive who can give information. I have a lot of info on family since my Great-great-grandfather's birth in 1812, part of which was provided by my dad's recollection of a family plot that none of us had ever been to. So I would check in with parents and grandparents first. Also, ask if they knew of any rumors in the family about it's origins. Sometimes those rumors end up being based on a truth, somewhere along the line.
Military and church records can be just as helpful as civil records in town halls and libraries. In some communities in the 1700s, churches were the only recorders of vital statistics. Also in generations past some states maintained records on members of the state militia, those records can be helpful until about 1880 or so. One thing I have found is that generally the further back you go, the less complete the information becomes... but not always. In my own research the worst period for records was 1760-1812. A lot can happen in 50 years...
Good luck on your searches, and remember that future generations of your family may be very grateful for the research that you may do now.