Tire/width reccomendations

Just bought a '98 328ic. It has 15" Continental tires on it. I've been thinking about changing to 16" or 17" wheels/tires. Does anyone have a tire reccomendation and what type of difference would I notice by changing the width?

Here is a website with all kinds of car math. Look about 2/3 down the page, you'll see a site for figuring tire size.

http://www.cobralads.com/car_math.html