You could have probably used the search function to find a thread answering this already.
Anyway, if you want to just win, any JP car can enter if I remember right. So you can just borrow a 787B or even X1 from a friend and win.
If you want to use a fair car, I would suggest the Nissan GT-R Super GT's, Lexus Super GT's, or the Nissan Nismo Z Super GT. They are easier to handle than the NSX's. If you still have trouble with any of those cars, you can just buy a stage 3 turbo and Racing Soft tires for them. That should make the event pretty easy.
As for the set up, set your downforce to maximum. That's the most important thing. For other settings, just search the GT5 Tuning section of the forum.
The rain in A-Spec isn't set to realistic, so Racing Soft tire is probably the best for the rain. Also, it does rain on the track, just not all the time. It's all about luck. If you don't want to drive in the rain, quit the race and restart until you don't see clouds in the sky.