First off, congrats.

You have a good mix in the proposed plan. Bangkok is a must-see, some mountains in the north (Chiang Mai) and some beach (Koh Samui / Phuket).

I echo that perhaps there is a little too much packing/unpacking and moving around. The only thing I would suggest is pick one of the 2 beach destinations. Either KS or Phuket.

Phuket can be a major beach destination. (Think "full moon parties" if you are at the right place/right time.) Koh Samui is a lot more laid back, island-feel kind of place. Your call.

Cheers.