The car for endurance should satisfy several criteria.
First, you must be able to achieve consistent lap times with it. That means that the car should be easy for you to drive, perhaps even sacrificing the sheer speed a bit. For example: if you choose the NSX, you should use front-stiff springs setup - that makes the car more understeery and slightly slower at some corners, but much easier to drive. Also don't tune your car to specific type of tires - that can backfire badly when tires start to fade.
Second, it should keep tires alive for as long as possible - that means you need light car (but not too light - mind first paragraph) with as much traction as possible. Also, avoid cars where tires do double the work, i. e. FWD and 4WD cars. For the same reason, your car should have sensible aerodynamics.
These are the requirements for fast cars.
Now about the fair challenge. As for me, I never use tires better than racing mediums (well, except for some experiments), and also keep the power not too high.
More certain examples: for enduros with LM cars (like the ones you are going to do) I use GT300-class cars, since they are light, nimble and easy to drive. Among the usual RMable cars the good choice might be some 450-500 hp MR cars, such as NSX and Venturi 400GT. The RX-7s are also good. That all being said, for Rome I probably still would go for something faster, maybe even like Esprit GT1 - just because AI are fairly fast at Rome.
For enduros with regular tuned cars I use sports tires and various cars. Seattle can be good fun if you're racing a muscle car (which doesn't satisfy any of requirements above, but the AI here is not too strong either), Grand Valley, I think, is good for S2000. Also there are some threads about enduros with different cars, although not all of them were close.