Hi Debgreg,
If this is your first visit to Thailand, I would suggest a package (that includes transfers). Several companies such as Trailfinders and Premier will do a mix 'n match to suit your needs, including flights (times and routes to suit), transfers and hotels. This frequently works out as cheaply, if not cheaper, than DIY - especially Trailfinders. We have tried DIY and "package" and have just returned from a "bespoke" package. We couldn't match the prices by DIY
Most of Thailand can expect good weather over the new year.
Don't miss two or 3 nights in Banglok - the Grand Palace and Floating Market - other things shown on this site are not to be missed. Many people prefer Bangkok on the way back (to do some shopping etc). Judge for yourself, based upon flight timings and your personal preference. Personally, we prefer Bangkok first.
If you choose Samui, you may find that Chaweng is a little too lively (yes seriously) for 13 and 15 year olds (but there again I am getting old!).
Samui is beautiful, Phuket is also, perhaps, worth considering. Hua Hin would probably be too quiet.
Christmas and New year can be busy, so do your research, find your flights and book soon.
It is a totally different experience from Goa - but to me, much more civilised and interesting.
Good Luck and Enjoy!
Peter