I think others have covered the seat assignment thing - I would definitely get that done right away just to be safe.
You mentioned something about getting something in the mail. Are you talking about paper tickets? I did not think that Airtran issued paper tickets. I'm not sure, but everytime I have flown, all I had was an e-ticket (which is nothing more than a confirmation number sent via e-mail). When you call to check on your seat assignments, you might ask about that if you are expecting tickets in the mail.
The only consistent complaint you will hear about Airtran is the fact that the do change their flight times fairly often, and are not always prompt about letting you know. I would make sure I checked the flight online fairly often just to make sure the times are still the same.
Other than that, Airtran is a pretty good airline. Someone mentioned the free XM radio, which is nice. They also have wireless internet available on every flight now, but there is a fee for that (I think about $10-$15 depending on the length of the flight).