Are you talking about driving around a track, or at a dragstrip?
If you're talking about driving around a track, stop worrying about what tires you're using. The biggest factor by far at the novice level is driver skill. An experienced driver in a slower car will beat a novice driver in a much faster car, 10 times out of 10. You're just learning now. Use whatever tires you normally drive on the street, and don't worry about "winning". Once you get a lot of experience, you can start thinking about less important factors (like moving up to track tires).
For street tires, the Yokohama Advan Neova AD07 (that's what it's called - I assume that's the tire you're talking about) isn't available in sizes to fit the NSX front. I can give you more advice on tires but again, upgrading the capabilities of your car when you're a novice isn't going to make you any faster; you're not using anywhere near the full range of those capabilities at this point in your driving career. Concentrate on having fun and learning a lot. Keep it up, and the "winning" will come along with the experience.
Also - are these events with an instructor riding in your passenger seat, with classroom sessions as well? Or is this an open track event, where you can learn lots of bad habits without anyone to tell you otherwise? Many such "open track" type events without instruction - sometimes called "test and tune" - are absolutely the
worst possible way to learn how to drive around the track faster.
And for heaven's sake,
NSXPO 2006 is in your part of the country this year - sign up! It includes two days on the track at Sebring. It's the perfect opportunity for a beginning driver to learn how to drive on the track, in an event consisting entirely of students driving NSXs, with instructors who are familiar with the car.