Actually stay with the smaller wheels! The smaller wheels, the better gear ratios you will have. Kumho and others make plenty of race tires that will fit that car. I'd try and get 205/55/14's for it. I think the unshaved / non heat cycled Kumhos run about $107. So basically you get the best of both worlds, better gear ratios and cheap race tires. I just raced an SE-R at my last autox on 14's and it handled great!
Race tires have an extremely stiff sidewall so don't worry about them not handling as well as a street tire, they'll blow any street tire on the market away no matter what size. The worst race tire is better then the best street tire. With more sidewall (well not too much more) allows you to adjust the handling of the car more through tire pressures.
The 14's also have another benifit, they are light! Having less rotational mass is always a good thing. The shorter the wheel, the less rotational mass you have, therefore making the most out of your car.
