Ellen, I haven't googled Tennessee's climate or species list, so I am probably not the best to recommend a specific tree. But in considering a tree along your driveway, consider its mature growth and spread as well as the roots (which is good to think about). If your driveway is concrete (which you mentioned) as opposed to asphalt, it will be stronger against errant roots.
I am not thinking the dogwood would have an aggressive root system, compared to some of your bigger species. And they can certainly be lovely.
I would also double check susceptibility to pests in your area. These sound like they will be making a landscape statement, not only a privacy barrier but perhaps drawing the eye as people approach. So a row of hardy AND beautiful trees will present a more pleasing appearance than ones constantly fighting off the "bug du jour".
Sylvia