What website would I go to do research on an old house?

Answer 1

Unless the house is somehow famous, this isn't well-suited to internet research.
The research should be done in three places, all local. First, the register of deeds office (or whoever records land ownership in your locale). This will give you the names and dates of ownership for all prior owners. Second, your local historical society, which may have records on the house or the previous owners. Third, the local newspaper, which may have articles on the same.
Unless the house is somehow famous, there won't be enough interest to have anything significant posted on the web.