You might find this helpful before you start on your quest...
Talk to your family. It makes no sense to spend days trawling through websites to find out your great-grandmother's surname if someone in the family already knows it. So first, talk to parents, aunts, uncles, cousins, grandparents and find out what they know. Most families have at least one individual who keeps track of the extended network of relatives, and if you can trace her (it usually is a her), you're off to a good start.
The only cast-iron rule of family history is that you start from what you know and use it to find out more. It is almost impossible to take a historical family and try to uncover what your connection might be. Instead, think of yourself as a detective, taking each item of information as potential evidence and using it to track down more information that in turn becomes evidence for further research.
Good luck and enjoy