To drive legally in Thailand, you will need a drivers license from your own country and an international driving permit.
Upon arrival at the Suvarnabhumi International Airport, there are many rental car counters including:
Avis
Budget
Europcar
Hertz
Sixt
Thai Rent A Car
Bizcar Rental
Chic Car Rent
I am use the the big three from the US, Avis, Budget, and Hertz. My philosophy is their insurance/crash policies are in place in the event of an accident.
One should not focus on price alone. But the service after an accident and whether you are financially responsible or not.
Driving in Thailand for foreigners can be very dangerous and the chance that someone hits or dings your car in traffic and drives off is very high.
We have had the side mirror on our truck broken off many times by motorcyclists that don’t bother stopping.
So it is best to choose a rental car company that has an iron clad policy on accidents.
One issue I have at Suvarnabhumi Airport, is when returning the rental car, it is extremely difficult to find the rental car return lot and you may waste an hour or 2 trying to get directions.
For the best prices, go right to the actual rental car company websites. Compare rates booking FROM your own country versus booking in Thailand for the best price.