Is it possible/easy to get to the site via public transit?
Yes. If you will come from Bangkok, go to Mochit Central Bus Terminal. Ride a bus going to Nakhon Ratchasima (Ratchasima/Ratsima/Korat). Tell the bus attendant that you will get off at Bogoso Mai. From Bogoso Mai (new bus terminal), there are buses leaving every hour starting 5 am to 8 pm to Phimai. The fare is 60 baht. Non-AC bus is cheaper.
Hope this helps.
Sorry i dont know for sure. But a taxi from nakhon ratchasima would be about 1000 baht each way (£20, $15) It will depend very much on where you start your journey - NR can be reached by train or bus from bangkok and there are some good hotels in the city of NR
Get quick answers from Prasat Hin Phimai (Phimai Historical Park) staff and past visitors.