As MvM indicated, vehicle setup is an important factor. So, it's a good idea to be sure your tires are in good shape, and if the car has been lowered, get the front and rear alignment checked, though without special parts such as Science of Speed offers, it's hard to get camber really right with significant lowering.
It's funny you should mention coming from a '94 Z28, as I have a 95 Z28 (going to my daughter soon, she's had a 99 Camaro for sometime, but the interior is way cheaper than my older Z for some reason).
With the Z it's possible to throttle steer the rear end around slower corners, and because of all that weight in the front, the front end tends to stay planted in spited of those antics. The NSX's mass centralization means that overall turn-in is quicker and more responsive. But in slippery conditions, especially with mediocre tires, that mass centralization means it's easier to put into a snap spin (never in my own case, fortunately). It's not as bad as a 911 with all that weight hanging out behind the rear axle, but it's something to be aware of. So, the NSX deserves a bit lighter touch- it won't understeer the way Z28 will if you just crank hard on the steering wheel. It will turn quickly (magazines having recorded up to 1.1G transient turn-in lateral acceleration in STOCK early NSX). And by Newton's first law, any object in motion tends to stay in motion unless an external force is applied.
The thing is, the NSX has much higher road holding capabilities than a comparison of lateral G's between it and the Z28 might indicate. So some time and respect to learn it's behavior will be rewarded. Rather than getting an MR2 to play with, I'd recommend signing up for a good track course in a formula trainer - these are rear midengine cars, typically with Mitsubishi or other small 4's, usually not making more than 180 HP. That doesn't sound like the hot ticket at first thought, but then these trainers only weigh about 1,000 lb. Russel Racing at Infineon Raceway does this north of the SF Bay area, and there are many similar classes available at tracks around the country. A two day course would be a nice way to spend a weekend.