My wife loves doing Genealogy! And yes, she has an Ancestry account
Believe it or not, the LDS have a fantastic site for doing genealogy and it's free (it's always a good idea to validate the work of others with concrete evidence). Ancestry is great too, and one benefit of Ancestry.com is that you can manually search the Census if a particular census hasn't been cataloged to include a search funtion yet.
My wife actually spent several months playing detective while manually sifting through hundreds of online census pages while trying to find my great grandfathers wife as she moved from place to place. It's a guessing game at times and the better you understand the historical culture, the greater your chances of finding who your looking for becomes!
Here's something we can laugh at though! I'm pretty sure that everyone in TN is related, and while my wife did her side of the tree, she found out that she was related to her mother in like three different ways
If your new to genealogy, have fun! And remember, if your great grand parents came over on a boat, the first place you may want to search is the passenger list. Oh yeah, it was pretty common for people coming over to slightly alter the spelling of their name too.... That's when the historical culture bit comes in ;)