Suvarnabhumi Airport is the Bangkok’s main airport. Many people fly to Suvarnabhumi Airport and want to immediately take the train to at Hualamphong train station to somewhere else. Here is my recommendation to get from Suvarnabhumi Airport to Hualamphong train station.
This is the easiest option. Taxis are waiting for you right in front of the airport and they can take you to anywhere in Bangkok. Taxi fare in Bangkok is relatively cheap comparing other big cities in the world. The weak point is it might take longer time to reach your destination because of the traffic jams. If your flight arrives during peak hours such as from 6.00-10.00 or from 16.00 to 21.00 and you do not have several big luggages, I do recommend you to take another option, use Airport Rail Link and MRT.
Airport Rail Link + MRT Subway
Airport Rail Link is an express train that connects you to city center of Bangkok. To go to Hualamphong train station, you just take Airport Rail Link to Makkasan Station. Then, walk around 5 minutes to MRT Subway (Petchaburi Station). Then, take MRT to Hualamphong Station. And, walk around 2 minutes from MRT to Hualamphong train station. See the map here.
I cannot say which option is faster and better. It depends on the traffic on the road at that time. If you are not in a hurry or come in group, taxi is better and also cheaper. If you come alone, Airport Rail Link plus MRT Subway is cheaper, and might be faster.