Get to the taxi rank queue outside the airport, ignore taxi drivers that offer you a lift ahead of the queue. Ask the taxi driver at the queue if it is a taxi meter if its not walk away. Taxi to pattaya should cost around 2000 baht.
I would do the bus if travelling with no children, otherwise a Taxi, You can get Uber in Bangkok but not in Pattaya. It was 1600 bhat in a Taxi from Pattaya to BK on New years eve. It takes around 1 1/2 hours in a Taxi and around 2 1/2 on the bus.