Never traveled before. Flight to NC. Best way to get transport from Raleigh to Durham?

I’ve never really traveled much so I’m not sure what to expect. I would be arriving in the Raleigh-Durham Airport and need a ride to Durham. Is getting a taxi what people would do? Or taking the bus? How much does each cost?

I come from a small town in the middle of nowhere so that’s why I haven’t a clue in this area. I’ve never taken a bus or taxi before. What do most people consider? Whats the cheapest option? Are round trip flight tickets cheaper?

Thanks for any advice.