Is it improved to go without delay to Phuket after nearing upon BKK’s Suvarnabhumi Airport as well as locate the made at home flight?
Can you take the Air Middle East moody from Suvarnabhumi Airport or from the opposite airport?
Or is it improved to take the luggages to the Bangkok hotel, leave it there as well as thereafter go to Phuket upon an additional day? We’ll have the lot of luggages as you have been starting to an additional nation afterwards.
Please advise

Sounds like a lot of fun! If your flight to another country leaves from Suvarnabhumi (BKK),you should fly direct to Phuket after arriving in BKK to avoid wasting time since you are not going to be there very long,then visit BKK before leaving Thailand.Either way, you’ll be in the airport 3 times,so whichever end of your trip will afford the shortest layover between flights (into BKK then to Phuket, or from Phuket to BKK, then your flight out of Thailand) would be the best choice.I have done this both ways, and I liked arriving into BKK,then flying directly to Krabi better.Either way, you’ll have lots of fun! Always smile when greeting, and say "Sawadee."
in order to avoid Bangkok becos you’re already exploring whole area, you can plan to visit Phuket directly, but another destination to share within southern part is to go to Samui Island or Trang Province (Haad Chao Mai/Chao Mai Beach) which also worthing to see both if you have enough time. I can guarantee.