Your Cayman is very well kept. Standard size tyres for an 18 inch wheel should be 235 x 40 at the front and 265 x 40 at the rear. Look for N spec tyres if possible.
thank you! I really want to wear 265 tires, but if the car height is lower than the original, the 255 tires are just about the limit for winter tires, so I'd like to get a 265 tire with a coilover installed someday!