How much will insurance cost for a nineteen year old female new driver living at home in rural Southwest VA?

That's almost impossible to answer. There are too many factors that need to be answered before you will get a correct answer. Go to http://www.progressive.com and get a quote, not only will you get a quote from Progressive, but they will quote you for many other companies as well. Getting insurance from larger companies like Progressive, State Farm, Allstate and Farmers normally costs 5-15% more then if you would go to a local insurance company.