Welcome to Mazdarotaryclub and we hope you find what you are looking for,
Even if the car starts instantly when cold the biggest thing to check with the RX-8 is to make sure it has a run down the road to make sure its nice and warm then turn the car off, leave for the same amount of time it takes for a tank of fuel to be put in which is around 8 to 10 minutes and only then restart the car.
If the car does not start cleanly straight away, walk away fronm the car as the engines compression will be low and only get worse.
The only real Achilles heal on the RX-8 is the ignition coils and you need to either check for invoices that the four coils have been changed or factor in the price of genuine Mazda coils (pattern ones invariably cause issues)
Aside from just these two things above just look and check the car over just like you would say a Ford Fiesta or any other "normal" car.
With prices of the RX-8 now, a huge amount of car is able to be bought for not much money.
hope this helps