How to find records/census?

I have been trying to find a town that my J�nke ancestors came from and everything I find just keeps saying Hanover, sometimes it even says town of Hanover. So now I'm still not positive they came from the city of Hanover but might as well start searching there to at least rule it out (maybe I'm just lucky and they are from there!)
Anyway can anyone tell me where to start looking for any records of their lives there? I'm looking for births in 1866, 1870, 1875, and 1887 and deaths and marriages that would have occurred in that time frame. Is there anyway to find emigration records?
And last, is there any kind of census or city directories existing for Hanover from 1860-the early 1900's?
Thank you for any help,
Sarah Junke