And the answer is.....SUSPENSION. The car you are bringing in from Japan probably has Japanese after-market suspension - designed for super-smooth Japanese highways. Rip them out and fit a compliant suspension set, one that won't end up rattling the fillings out of your teeth.
The profile of the tyre will provide some softness to the overall ride quality, but nothing in comparison to the spring/shocker combo fitted to the car.
For wheels, stick to 17" rims. 18s might "look awesome", but they are heavier, and contribute to an increase in unsprung weight of the car; that, in turn, detracts from the handling performance.
17" tyres provide the best combination of performance available for $$ spent. Generally, 235/45x17 tyres are the most affordable of the low-profile performance tyres around, and will fit the majority of aftermarket rims that might be suitable for your car.