On the first day of the tour you need to be in Demre. Therefore, you can arrive there the day before from Antalya or Dalaman; the journey will take 3-4 hours by public transport. You can also arrive in Demre early in the morning on the first day of the tour, but it may be difficult as the day is busy.
It is better to fly back the next day after the end of the tour. The journey from Kas to Antalya or Dalaman takes 4 hours by public transport.
You can take air tickets without luggage and get by only with hand luggage, since you only need to take comfortable summer things with you :)