Originally Posted by
MmeD
Seems like there is a train to the airport (with the airplane icon) at 1600, 1610,1617, 1630, 1640, 1647.
Be aware that some of those trains are Rapit express trains that take 37 minutes (the ones with the Beta above the airplane icon. Some are just express trains (times printed in orange typeface) and some are ordinary local trains that stop at every station (times printed in black).
The 16:00 Rapit, will get you to KIX at 16:37.
The 16:10 departure takes 10 minutes longer - reaching KIX at 16:57.
The 16:17 departure reaches the airport later than the 16:30 departure so fuggedaboudit
For more guidance on which trains to take, check the Hyperdia website, which will prioritize trains by their arrival times at KIX.
Originally Posted by
MmeD
There are few other trains running in between. Are those not stopping at KIX at all or are those just slower train but will stop at KIX?
The railroad splits into two branches at Izumisano. Some trains follow the tracks to KIX (those with the plane icon), and others go to other places - such as Wakayama. If you find yourself on a fast train that's headed to Wakayama, get off at Izumisano. From Izumisano, it's a short distance to the airport.
Originally Posted by
MmeD
If the train is running that frequent, would it make more sense for us to buy tickets when we arrive at the station as supposed to purchasing them in advance?
With your tight schedule, I'd really try to have your tea earlier. I'd hope that a nice hotel would find a way to accommodate your request. And I'd reserve a ticket on a Rapit train. YMMV.