Hi Linda,
You have to fly to Phuket as I'm pretty sure that the train does not go all the way there. As for Chiang Mai, you can catch a train there but it is around a 12 hour trip which will mean cutting into your holiday a bit. Depends whether you really like train rides and can spare the time. If you have a look at Air Asia's web site they are doing some really cheap deals to both these places. Can't remember the travel dates though but it is worth going and having a look.
The places you mentioned in Phuket - are you planning to stay at all of them? If so I personally thimk that you will spend so much time repacking and arranging tranfers which are not cheap!
If you give more information on what you hope to do/see there and also in Bangkok, people might be able to recommend the best area to stay. It might be better to arrange a guide/driver for the day to go to other areas.
Also how much were you planning to spend per night on accomodation? This way people can recommend places to stay.
Definately go to Ayutthaya for the day. It is a great place to see.
As for booking accomodation - I think January is high season and if so you will need to book. Maybe someone who has been there at this time can give you a rough guide of how soon to do it.
Happy planning - hope this helps a bit

regards

Karin