After going through several posts on the forum, I decided to try a new tyre size on (GT2 size) my 2002 996TT stock rims. Initially I was looking for Nitto NT-01 but found a set of Michelin PS2.
Front: 235/40/18
Rear: 315/30/18.
Initially I found out that the inner edge of rear tyre was touching the plastic covering of the wheel housing, so I had to bend the metal bracket a little bit that holds the plastic housing of the wheel to avoid rubbing. The car has stock suspension and not lowered. Front wheels had no problem.
So far no PASM issues, road noise level is minimum, and better handling. I believe I can use this settings for regular street driving and occasional DE/Autocross.
(I have my Sumitomo HTR ZIII 295/30/18 (2) with 75% thread left available for selling, in case if any one is interested)

 

If you run the same GT2 tire sizes on GT2 wheel specs on a stock TT you shouldn't have any rub...TT wheels sit a bit more inwards

 

Did you not like the Sumitomo HTR ZIII ? I've never tried them, just curious.

 

I think Sumitomo is a good tyre if compare the price, less than half of a Michelin PS2 price. They are not as sticky as dedicated track tyre, noise level is pretty low on regular street driving. Overall for the price I think they are very good tyre.
I had Michelin PS2 225/40/18 (stock size) in the from and bought the Sumitomo 295/30/18 to match with stock rear size. but I guess the diameter of the 295/30/18 of PS2 and Sumitomo are different and PASM was acting up frequently on hard cornering, DE events. So I decided to have a dedicated set for track/autocross.