Welcome to Pattaya Aaron,
From Bangkok to Pattaya by plane is no direct flight if you want to fly you have to take Bangkok Airways fly to Phuket or Samui then to Pattaya. Or from Bangkok to Koh Chang(Trat) then you have to take a car/bus to Pattaya.
So I suggest you to take a car/bus. I have one travel service it names "Bell Travel Service" it takes you from Bangkok Airport (Suvanabhumi airport) to your hotel in Pattaya. for only 7-8$ or 200 Baht. At below you will see more detail.
Bell Travel Service Bus to Pattaya
Bell Travel Service run a bus service between Suvarnabhumi Airport and Pattaya. They also service Bangkok and Don Muang Airport (the old airport.) Here is the information between the airport and Pattaya.
You will need to reserve your seat in advance. They like to have at least seven days notice, if possible. Their staff will wait for you on the first level near door number 7 which is near the Tourist Police counter. Look for someone with a sign reading 'Pattaya - Bell Travel Service.' The bus will be located nearby.
Busses from the airport leave at 08:00, 10:00, 12:00, 14:00, 16:00, 18:00.
The fare is 150 Baht and includes transport to your hotel in Pattaya. The fare is paid as you board the bus.
Return times are 6:00, 9:00, 11:00, 13:00, 15:00, 17:00, 19:00.
The return is also 150 Baht and includes being picked up from your hotel.
Contact details:
Phone: Bangkok - 02 747 4673, 02 747 4675
Phone: Pattaya - 038 370 055, 038 370 056
Phone Airport - 089 449 8843
Email: rrc_bus@hotmail.com
http://www.pattayanewbie.com/bell.html