Originally Posted by DevilBucsFlyer
There is a train station right at the Bangkok airport if that's an option for you. Not sure about busses.
Not a (practical) option: Don Muang is on the north/northeast line and it would take a minimum of two transfers to get to Thonburi station for southboard trains.
Take the taxi to the Southern terminal and just get on the next bus out. Don't worry about the schedules, the buses are rarely full.