For the average consumer, the aspect ratio is one of the most important numbers. The larger the aspect ratio, the taller the tire's sidewall. A tall sidewall is great for a quiet, supple ride, because the sidewall can flex and distort easily when running through potholes or over expansion strips. Aspect ratios of 60 - 75 are considered tall and are common family cars and minivans.
A short sidewall will benefit you in the handling department, reducing sidewall flex and better connecting the wheel rim to the tire tread. It also produces a noticeable increase in ride firmness and tire noise. Hide speed cornering does not produce the tire howl that a taller tire will. Aspect ratios of 35 - 55 are considered short and are commonly found on sports cars.
Tread width is the other important factor in determining a tire's ride characteristics. A wider tire has more contact area with the road than a narrower one, and therefore has more grip, which is perfect for increasing handling limits. A wider version of the same tire will generate more noise and more rolling resistance, which will slightly lessen fuel economy, and it generally doesn't work as well in the rain, a narrower tire tends to slice through water.