You actually have a few choices for your ride to Pattaya. You can go the cheap route take a taxi to the bus station, catch the bus to Pattaya, and then get another taxi to your hotel.
You can share a ride either with someone you met at an online Pattaya forum or go with a group in a 6 9 passenger van. I have made a couple of good friends sharing the ride and the cost with one other person and have had nothing but bad experiences sharing a van with 8 others.
My preferred method of traveling from the Bangkok International Airport Suvarnabhumi to Pattaya is to book a ride online in advance and have the driver waiting for me when I arrive. I have found a reliable source at a Pattaya forum and have used him for the past 6 years and he has never let me down. He is always waiting for me right outside where you pick up your luggage. I have never been disappointed.
There is one more option the notorious taxi mafia at Bangkok International. These are the pests that block your way as soon as you leave the luggage carousel. They have a clipboard in hand and will pester you even if you tell them that you already have a ride booked. They charge about double...