The most important decision you'll make is what cookware material your set is made from. Cookware is commonly constructed from aluminum, cast iron, stainless steel, copper, nonstick chemical compounds (Teflon) or a combination of several materials. As you might guess, each type of cookware surface has its pros and cons as it relates to cooking, cleaning, durability and storage.
Aluminum cookware is cheap, for example, but it is not very durable and I wouldn't recommend buying a fully aluminum set. Stainless steel pots and pans will better withstand abuse and won't warp or dent like aluminum. Stainless steel is also a slow conductor of heat, which is why steel pans often have a core made from a more conductive material such as aluminum or copper.
For most people, stainless-steel cookware fitted with an aluminum core will be the best material composition for a set. Materials such as copper and cast iron have advantages but also some serious pitfalls. Cast iron and carbon steel are both a bit heavy and require slightly more involved cleaning and care, so you might not want an entire set. Copper cookware is also more difficult to care for and generally costs much more than its stainless-steel counterparts.
Nonstick is another popular option. I recommend having at least one nonstick skillet -- either Teflon or ceramic -- for eggs and other sticky foods. That said, you'll never be able to sear food using nonstick the way you can with other materials, so keep that in mind if you're opting for a fully nonstick cookware set. It also won't last as long since nonstick coatings break down over time.