Winter travel No. Calif to NC via the South

Planning a cross country trip to visit friends and family. Starting in NO. Calif. ending in Greensboro, NC. Stops in Phoenix and Bryan/College Station, Tx (Go Aggies). Have never driven the route from Tx to Greensboro but imagine we would stay south to Atlanta and then turn left.
Any advice appreciated as we will be leaving California in early December and returning in mid January.