The airport bus is good. Its only 100 baht and takes you right to most of the hotels. If you want a real public transportation experience, there is an airconditioned bus that goes from the airport to the bts. From there, you take the bts to Sukhumvit. I forget the bus number. The cost ends up being about the same.
First time in BKK for me I just followed the instructions at this link http://bangkoktonight.com/info/bangkok_airport.shtml It will take you through the airport to the correct taxi stand and give a newbie all the help you need. I used it on my first trip and it is great.