Why You Need a Chef's Knife
The chef's knife will be used the most in your kitchen. You will use it for chopping, slicing, dicing, and cutting. Professional chef's seem to choose a 12 inch blade for their chef's knife but the home cook can usually get away with an 8 inch blade chef's knife for all intensive purposes. You'll need to hold one of each size to determine which would work best for you.
You should always use your chef's knife in combination with a cutting board
Why You Need a Paring Knife
A paring knife is used when you need to do more controlled cutting in the kitchen such as when you will be peeling and cutting delicate fruit, or for cutting and chopping smaller ingredients such as garlic. You'll also use your paring knife for detailed cutting such as when you need to slice vents into your pastry dough, or for removing ribs from fresh peppers.
Due to it's small size and precision cutting you should be able to do things like peel apples while holding the knife and fruit in your hands.
Paring knives vary in length size and usually run anywhere from 2 1/2 to 4 inches long. Again, it is recommended that you hold several different sizes in your hand to determine which length is the most comfortable for you.
Why You Need a Serrated Knife
The saw-like teeth of a serrated knife make it easy to slice through things that are hard on the ouside but soft on the inside such as a loaf of crusty French bread.
The serrated knife is designed to be used like a saw, gliding the knife in your hand, back and forth, with each pass cutting deeper into the food item.
Serrated knives come in many different lengths. I find the 5 inch length to be the most comfortable and useful for me. As a guide, you should choose one that will be long enough to cut through a loaf of bread.