Although Bailey's is good stuff, I prefer St. Brendan's cream liqueur. It's also a bit less expensive than the better known Bailey's. Brendan's has a thicker consistency and the alcohol adds a bit more bite so it isn't quite as sweet as Bailey's. For the best cup, though, I would definitely stick to one of these two Irish creams, since most other American knock-offs are far inferior in flavor and thickness.
You can use any type of coffee, but I prefer a strong black brew. Avoid instant coffee at all costs! Stronger and bolder blends work best because they can stand up to the flavor of the cream liqueur and whiskey. Speaking of which, use a good Irish whiskey. Jameson's seems to be the popular choice, but any smooth whiskey will work.
You can top the whole thing off with some good quality cream, if you prefer, or add a sprinkling of chocolate curls or cinnamon.