Buy This Cookware Set: Kirkland Signature 14-Piece Hard Anodized Cookware Set
While the most important thing you can do to improve your cooking is to buy a better knife, the second most important thing is almost certainly to buy better cookware. If you've only cooked with cheap, thin pots and pans before, you'll be amazed how much easier things are when you have a couple of sturdy pots and pans to work with. Your onions won't burn anymore and your eggs will cook evenly. Your pans won't warp until they're curvier than Scarlett Johansson. In short, good cookware makes good cooking much easier. You need some.
Two caveats before I offer my recommendation:
1. I'm assuming you currently have no adequate pieces of cookware. Maybe you're in your first apartment after college and have never bought cookware before or you own a cheap set that is now fit only for the scrap heap. If you do own some decent cookware, you're probably best off filling in the gaps in your collection with individual items rather than a whole set.
2. You plan on cooking at least some serious, multi-component recipes, or at some point you plan on having more than a few people over for dinner. If so, you'll appreciate having a lot of cookware, and a set may be right for you. If not, you're probably best off just getting a big pot, a small pot, a big pan, and a small pan.
On to my recommendation...
I love Costco. Probably not as much as I love Trader Joe's, but still quite a lot. The best purchase I've made at Costco (and maybe the best purchase I've ever made anywhere) is this cookware set: the Kirkland Signature 14-Piece Hard Anodized Cookware Set.
I agonized over this cookware decision. I knew I wanted a set, but with a limited budget most of the recommended cookware by All-Clad or Calphalon was way out of my price range. I also considered this Wolfgang Puck set, but had concerns about the durability of the disc bottom.
Thus I went for the Kirkland Signature, and I couldn't really be happier. You can follow the link for all the details on what's included, but the most important thing is that the whole set only costs $150. The direct comparison is this Calphalon set for almost $600, and that one doesn't even include as many pieces. I would honestly recommend to someone that they pay the $50 Costco membership just to buy this cookware set. It's even a Consumer Reports best buy.
Kirkland Signature is Costco's house label, which means that you're paying much less of a markup. The cookware is made of anodized aluminum, which is great because aluminum is almost as good as copper in terms of conductivity (higher conductivity means the pan heats evenly). Regular aluminum reacts with acidic food (which is why cookware is often lined with non-reactive stainless steel), but anodized aluminum has been treated with electrolysis to form a corrosion and stain resistant surface layer of aluminum oxide.
The only caveat is that the cookware is "non-stick", meaning that a non-stick coating has been bonded to the surface. Why is non-stick less desirable? For one thing, non-stick is less durable, and won't last long if you don't treat it well. I treat my cookware well, only using non-metal utensils and washing by hand with non-abrasive sponges. After over a year of hard use, my cookware set is still in great condition. I expect the set to last many years more, which is almost unheard of for non-stick cookware. And Costco has a 100% customer satisfaction return policy, so if the set breaks down too quickly you can always return or exchange it.
The other problem with non-stick is that food doesn't brown very well in the pan. Browning means flavor (see "maillard reaction"), so cooking with non-stick can mean less flavor when you make pan sauces or braising liquids by deglazing the fond (the brown bits) that has built up in the pan while cooking meats or vegetables. Saying all that, the Costco set browns better than other non-stick pieces I've used. Plus, non-stick pans are really easy to clean, which is a huge bonus when you have no dishwasher and do everything by hand, like I do.
So buy the Kirkland Signature 14-Piece Hard Anodized Cookware Set. Your friends will never guess how great a deal you got on those gorgeous pots and pans when they're gorging themselves at your dinner parties.
UPDATE (12/13/06): The set is no longer available on Costco.com. I would suggest checking your local Costco to see if it is in stock, or buying a set off of eBay.