There is an EXCELLENT article about choosing cookware HERE.

First thing, I would advise very strongly against buying anything in sets. Chances are that all the pieces won't meet you're cooking style.

Instead, individually choose the make, model, and material you need for the purpose. Personally, I don't use "non-stick" for various reasons. But some people feel they should have at least one non-stick skillet for certain recipes. For low & slow cooking, a cast-iron Dutch oven is the cats meow. And for day-to-day cooking it's hard to beat clad stainless. If you don't mind the weight, the best cookware is cast-iron, either porcelain clad or naked.

In the day-to-day you might choose one brand/design for skillets, but another for saucepans, still a third for larger pots.

Consider your budget, too. The most expensive isn't necessarily the best for your purposes or budget. Indeed, one of the so-called top end companies has a really poor customer service level. So you have to consider that, as well.

Make sure you handle the item in the store exactly how you will on the stove. If you're a lift it, shake it, flip it kind of cook then one handle design might be better than another for you. If you're a slap it on the stove and leave it be type, then handle design is almost irelevent. Consider, too, the weight and balance of each piece, and how comfortable it is in your hand. Etc.

Most of all, choose pieces whose design you are happy with; you're going to own them a long time.

Here's a repost of my $.02:

I have bought individual items as well as sets; one advantage to a set of pots is that you learn about the responsiveness of one pan, it's pretty much the same across that line. That's not that big an advantage, to be sure. After all, you're gonna be watching the pot anyway, right?

Restating some of the points of earlier posters, you'd do well to buy individual items (of very good quality) that perform the function you want that pot to do.

If I were to stock a new kitchen today, here's what I'd start with:

A couple of enameled cast iron dutch ovens of size appropriate to your needs. Those babies are some of the most versatile items you can get. Very worthwhile if you do a lot of braising.

A nonstick frypan or two for sticky stuff like eggs (Sam's Club has some Tramontina skillets, a set of 3 for around $30)

A black cast iron skillet for searing meats

A big stockpot for soups and boiling pasta.

A couple of saucepans: if you really do make fancy sauces then it's worth it to get very responsive pots. If, like many people, you use saucepans just to warm things up, the quality is not as critical.

One item most people don't think of is a pressure cooker. I'm sold on them, and wouldn't want to have a kitchen without one. If you think of pressure cookers as those things that your mom told you stories about them blowing up, do know that they've improved them greatly in the past couple of decades. A Kuhn Rikon 8 qt stockpot/pressure cooker is an awfully nice indulgence and you can cook a great deal of comfort food quite quickly. Check out any of Lorna Sass's cookbooks and missvickie.com if you are at all interested.

Whatever you get, get items you will enjoy using.