What to look for - There are several materials from which to choose as listed below. The criteria are the same for all. Pots should be heavy enough so that the entire bottom surface sits flat on the burner. However, don't choose those that are excessively heavy and are a burden to maneuver. Be certain that the handles are designed to stay cool and are ovenproof. And look for those that withstand high oven temperatures. Of course, price is a consideration, but keep in mind that a really good pan will last a lifetime with proper care. When you have decided which type(s) you need, then choose the styles you will use.
Types of Cookware
Copper - Copper is an excellent conductor of heat which is why it is the choice of many professional chefs. The interior is usually lined with stainless steel to prevent reaction from acidic foods. Good copper pots are quite heavy and require frequent polishing to keep their shine. The biggest drawback is the price. They are very expensive, costing nearly twice as much as the same pan by the same manufacturer in high-quality stainless.
Aluminum - Aluminum is another excellent conductor of heat but, like copper, can react to acidic foods. It also scratches easily. Therefore, a high-quality aluminum pan undergoes a process called hard anodization, in which the aluminum is treated to prevent it from reacting or scratching. See 'Stainless Steel' below for other ways in which aluminum is used.
Stainless Steel - Stainless steel, although lighter in weight and easier to maintain, is a very poor conductor of heat and therefore not recommended unless combined with copper or aluminum. The best of this type has a stainless steel interior and an aluminum core that is sandwiched between the inner and outer layers on the bottom and up the sides of the pan. This gives the desired weight and optimum heat conductivity while preventing reaction to foods and providing easy maintenance. Most of the pots and pans I use are stainless steel with an aluminum core. I love them.
Nonstick Pans - No matter what other type of cookware you select, every well-equipped kitchen needs some nonstick pots and pans. It makes cleanup so much easier and less fat is needed in cooking. However, do your research before purchasing. There are different types of interior surfaces available and teflon, which works the best, will wear out eventually, so don't feel that you need to buy the most expensive. Look for the same qualities as in the other pots, such as weight, heat conductivity, handle durability, and temperature limitations. Be certain to follow the manufacturer's recommendations for maintenance and heating, as most need to have some oil in them before they are heated, even if just a bit of cooking oil spray.
Cast Iron - I would not go so far as to say every cook needs cast iron pans, but they really are great for some types of cooking. I have an old set that was my grandmother's, perhaps her mother's. They are at least 100 years old. They have been through both fire and flood. It was not fun cleaning them after either of those events, but I guess they are indestructible. All cast iron must be seasoned before use which is a process of oiling and heating in the oven. Once well-seasoned, they are virtually nonstick. They are extremely heavy, great conductors of heat and totally temperature proof. They are food reactive. I remember making turnips in one and the turnips turned dark purple and took on the flavor of the iron.
The cookware below is what I consider basic. If you are like me, you will want other cookware. Don't forget a roasting pan and grill pan. Electric pans are useful, especially a crock pot. Most skillets do not come with lids. They can be purchased separately if needed. You can use lids from the saucepans and other pots or purchase less expensive lids. If you decide to purchase new cookware, don't discard all of the old. Keep some for the outdoor grill. They come in handy, especially during prolonged power outages. But even on the grill, beware of handles that cannot stand the heat.
Skillets - These are essential. You should have some nonstick for frying with very little oil or for frying delicate foods such as eggs and fish. But you need some heavy stainless steel with aluminum core for high-heat searing and other frying. Skillets generally range in size from 6 to 12 inches. Choose a small, medium and large as needed.
Saucepans - These also come in a variety of sizes from 1 to 4 quarts. I even saw a 6 quart but, at that point, I would use a stockpot. I have 1 quart, 2 quarts and 3 quarts. I prefer the heavy stainless with aluminum core rather than nonstick for most preparations because they clean very easily. Saucepans are used for sauces, cooking vegetables, and reheating foods that contain liquid.
Sauté Pan - This is essential, at least in my kitchen. I have two sizes; a 10-1/2 inch (3 quarts) and a 13 inch (6 quarts), both stainless steel with aluminum core. I make a lot of pasta and they are great for pasta sauces. They are large enough to add the pasta to the sauce to combine before serving. They are also great for shallow frying because the sides are a bit higher and straighter than skillets. Another excellent use is for braising, such as pot roasts, or large amounts of vegetables.
Stew or Soup Pot - This pan will have different names depending on the manufacturer. Sometimes called a casserole, soup or stew pot or Dutch oven, they all serve the same purpose. Basically, it is like a short, wide stockpot. I recommend a 5 to 6 quart. That is a good size for soups, stews, large pot roasts and oven braises when cooking for family. However, I also have a 4 quart for smaller preparations. Make certain it has a tight fitting lid.
Stock/Pasta Pot - Can't do without it. You will need at least an 8 quart. This is sufficient for large amounts of soup or making homemade stock and essential for cooking one pound of pasta. The one I have has a colander insert for draining pasta and a steamer basket. Although less expensive and of lesser quality than my other cookware, it is more than adequate to serve its purpose.