Agree with mr.cycling there's no saving time and cost for catching bus from Chiangrai to Chiangmai. Bus from Chaingrai to Chaingmai is approximalty 3 hours + wating to board the planes at Chaingmai airport + cost of bus between Chiangrai to Chaingmai + taxi from bus stations to airport.
I would go from Chaingrai to Krabi via BKK save time and cost.
Jumping back to your original question, which we all sort of glanced over ...
Thai Airway and Bangkok Air are full service carriers, baggage, snacks included in the airfare. They both go via Suvarnabhumi where you have more food options during your layover.
If your budget is not restrictive and you plan to fly the full service carriers, I might suggest Bangkok Air as they allow lounge access while you are laying over in Bangkok.
Yes if budget allowed go with Bangkok airways. They have comfy lounges with snacks, drinks and wifi for you to use while waiting for boarding You only need to show boarding pass.
Yes from BKK go up to Chaingrai first and then catch green bus down form there to Chiangmai. Its make more sense, time save and cost.
What are the Add Ons?