I believe both are possible in native speech, although "going" could be found incorrect by some. Notice that you're making a choice between taking the slowest train and going by air and the taking of the train is (correctly) expressed with the infinitive form of the verb. Why not use the same form for the going by air?
Please note that I'm not a native speaker, and that may and often does influence my perception of English grammar and usage.
Student or Learner