Yes.

The airport bus is not all that much less expensive, and
a much greater hassle. Don't even think about the train,
especially if you are going to Sukhumvit.

If you want to check on airport pickup by your hotel,
please do... but I expect that it will be at least 4X the
cost of a taxi. Using the taxi desk as described above
(exit through customs, turn left, walk past all the touts,
go outside, and you will see the booth), and it will be
painless and reasonably efficient. Pay the tolls to the
driver (60 baht) for the highways.