I'd recommend the Michelin Pilot Sport Cups for your application. They are the only R-compound tire that come in the sizes that preserve reasonable front-rear balance without an aftermarket sway bar. Get 205/55/16 for the front and 245/45/16 on the rear. They're expensive, but will greatly improve grip. Bear in mind that they come with very little tread that will wear down quickly, so long before they really wear out and are still good to use on the autocross course, they will be illegal (in terms of tread depth) on the road. I use The Tire Rack for my tire purchases and recommend them.

I recommend a track trailer solution, here's what I did to build a low cost trailer. And here's one of the hitches you can use. .

 

You can use the Kumhos on the street with no problem.

For track use, the 225/50 fronts and 245/45 rears pretty much DEMAND a large front swaybar to tame oversteer. You can use the 265/45s on the rear and give up some acceleration (about 4%) and raise the rear 1/2". That combo has more rear tire than stock. The Kumhos are considerably cheaper than the Michelins but it's your call...

 

Thanks for the great tire advice. Cheaper would probably be better since for at least the time being I would be using them for driving on the street to and from the track (and changing them at home), and they would be wearing faster.

I think if I were to get into trailering, then I would probably trailer the whole S2000...

I didn't realize that 265/45 was a possibility for the rear.

Thanks, and Kind Regards, Chris