For just a general cutlery set, you need at least one of each of the following: A large chopping knife, a serrated bread knife, a small peeling knife and a filleting/boning knife. It is also a good idea to have several steak knives for when you're eating.
There are a variety of different materials the knife blades are made of. One of the most common higher quality materials is stainless steel. Stainless steel knives resist corroding, and are fairly strong, on top of being relatively cheap compared to other high quality materials. High-carbon stainless steel is especially nice because it adds a little flexibility.
The material used to make the knife handle is much more important than you might think. Wooden handles have a tendency to rot or corrode. A corroded handle will make the blade fit loosely, which can be dangerous. Look for micarta and titanium handles because they are best for a mix of durability and strength. They are less likely to break than many other handles and are not overly heavy.
The way that a knife is designed is important. Look for rivets that are of a similar quality as the blade and are even with the handle in order to avoid snags. The part of the blade that goes into the handle (called the tang) should go all the way through on both sides. Many knife tangs only go part of the way through the knife's handle or only go through on one side. This may cause the blade to come loose.