There are air-con busses leaving from Mo Chit Northern Bus Terminal in Bangkok every 30 minutes, daily from 7 am to 11pm.You can go to the bus terminal, take the MRT underground to Kamphaeng Phet Station and from there a motorbike taxi (30 baht) to Mo Chit Bus Terminal.
There is no train station in Sukhothai. If you still want to take the train as close to Sukhothai as you can, I recommend traveling to Phitsanulok (5 hours) and take the bus from there to Sukhothai (1 hour)
Sukhothai airport is located about 40 km north of New Sukhothai. You can flight from Bangkok by Bangkok Airways.The one way fare is from 2,000 baht and the flight takes about 70 minutes. Bangkok Airways offers transport to New Sukhothai, 30 mins, 120 baht one way.
motorbike