Whatever type of pan you pick, it should above all be sturdy. Thickness means that a pan will not dent, warp, or have hot spots (which cause food in one area of the pan to cook faster or burn before everything else is done). Thinner materials won't hold heat evenly. A deeper pot should hold heat all the way up its sides; a weighty one will also be more durable and withstand frequent use and washing.
The three basic pots you need to start your collection: a two-quart saucepan, a 10-inch saute pan, and an eight-quart stockpot. They'll cover just about any cooking task, and if you buy high-quality pieces, you'll have them for a long, long time. And if you're buying only three, you can get the best.
StockpotWhile this should be of good quality, it doesn't have to be quite as hefty as the other two. Although you want it to be sturdy, you'll be using it mostly to boil water for pasta and blanching or steaming vegetables, so you want to be able to lift the pot once it's full of water. Something in midweight anodized aluminum is a good choice, since you may also want to use your stockpot to make large quantities of soup, stock, or stews. (If you'll be using it mainly for boiling water, buy the cheapest you can find.) Anodized aluminum is treated with a strengthening protective coating and will perform well without costing a fortune. The handles on a stockpot should be big enough to grasp firmly. If a colander insert doesn't come with your pot, consider buying one separately. The insert is not crucial, but it makes it easier to lift out pasta or vegetables.
Sauté PanFor searing and sautéing meats, vegetables, and chicken, pick a stainless-steel sauté pan. This pan will prove to be your most versatile. Not only can you sear anything to a golden brown but you will also be able to make a quick sauce with pan drippings. You can cook a whole meal and have only one pan to wash. The three-quart saute pan is the right size to make risotto and homemade pasta sauce, or even do some deep-frying. It's great for stir-frying, so you won't need a wok. With this type of pan, it's important that the base be thick enough. A thin pan may buckle, making it hard to cook food evenly. Most good-quality stainless-steel pans have an inner core of aluminum or copper to enhance steel's relatively poor heat conductivity. Handles should be heatproof and secured with heavy-duty, noncorrosive rivets. Stainless-steel, wood, and plastic handles all stay cool on the stove-top, but only steel and cast iron are ovenproof (wood will char, and plastic will burn). A pan with a steel handle, then, gives you the advantage of being able to finish the cooking in the oven. (And, obviously, use mitts when removing anything from a hot oven.) Lids should fit snugly (a tight-fitting cover helps keep moisture in the food), with a secure knob that is heatproof.
SaucepanA two-quart saucepan is the right piece of equipment for making sauces and rice, or for reheating soup and pasta sauce. For handling all these tasks quickly, your best choice is a pan made of copper. It will look warm and inviting hanging from a rack in a country kitchen, but it has more going for it than mere beauty. Copper is extremely responsive to temperature changes, so it heats up and cools down immediately as you turn the stove dial. This means it's especially good for making delicate sauces and candies or melting sugar. Look for a cast-iron or bronze handle with sturdy stainless-steel rivets. Apart from the aesthetic consideration, don't worry about polishing copper pots. Tarnish does not affect performance. Copper cookware is usually lined with stainless steel or tin (exceptions being preserves pans and bowls for beating egg whites). Easy-to-use copper polishes are available in cookware and hardware stores.