Choice of cookware is as important or maybe even more important than choosing a range. Cookware that gets heat evenly to where you want it and not to where you don’t is a wonderful thing (and likewise, the opposite is… the opposite). So here a few quick thoughts. This is far from definitive and its worth your time to do further research.
Nonstick – The only durable non-stick surface is well seasoned steel or cast iron. People are often afraid of these or think that they are a gob of work but they are not a lot of work and once you get use to using them you’ll never want to go backwards.
Nonstick Coated Cookware – The man-made stuff, be it PTFE/PFOA (most non-stick including Teflon), Ceramic, Silicon, Superhydrophobic or other is NOT durable. These should be treated as disposable and once scratched or showing signs of peeling, significant wear or loosing non-stick ability should be immediately tossed as they are no longer considered safe. A good non-stick fry pan lasts us about one to two years.
These coatings are relatively safe when used correctly and so long as the upper surface is fully intact and not scratched or otherwise damaged. Always pre-heat with low to medium heat and always with oil in the pan. ALWAYS avoid any temps over 500°f. NEVER use metal utensils or abrasive cleaners that will scratch the surface. DO use soft plastic or wood spatulas and spoons. If you stack them (not recommended) then place a cloth or paper in the pan to protect the non-stick finish from scratching. DO NOT wash in a dishwasher. Do wash carefully by hand. DO toss them when the coating is no longer perfect. PFOA is the highest risk but most manufacturers stopped using it over the past few years. If you have any PTFE/PFOA non-stick made prior to 2014 you should probably replace it.
I think the only nonstick coating that we have in our kitchen is a couple of skillets used only when necessary such as for scrambled eggs. Pan frying meats or veggies is best done in a steel or stainless fry pan as it is impossible to get a proper sear and caramelization with non-stick both because non-stick is… non-stick (a slight bit of stick is necessary) and non-stick coatings cannot be heated to high enough temps (and if you do it gives off noxious fumes). BTW, a little sticking to the pan for steaks, shrimp and other things is good. Griddles should be seasoned steel or cast iron – the thicker the better.
Clad/Tri-Ply vs Disk – Disks are thicker than clad or tri-ply and do a much better job of spreading heat out evenly but they don’t go around curves very well.
Skillets, Fry-pans, Sauciers and maybe tapered sauce pans should be clad. These you want to have as even of heat as possible on the bottom AND running up on to the sides.
The rest including Sauté, Sauce Pans and Stock Pots should be disk. These you want very even heat across the bottom of the pan and out to the edges but NOT up on to the sides. The disk will do a better job than clad of providing you with even heat across the bottom of your pan where you want it. This is doubly important for induction or sealed burner gas (most consumer ranges) that produce very uneven heat but is still noticeable on good open star burners. The disk should extend to the edges of the pan and not stop short.
Aluminum – Not such a good choice. Aluminum cannot be used with anything acidic (think tomatoes, tomato sauces, anything with lemon or other citrus, etc) and the aluminum leaches in to food (whether enough to be a health problem is debatable but I do know people in the health research world who avoid aluminum). You’ll see a lot of aluminum cookware in restaurants, but only for specific tasks. They use them because they are inexpensive and they may have twenty 2qt sauce pans for one single purpose where they know the taste will not be affected by Aluminum (and otherwise they’ll use stainless or steel). Anodized aluminum is probably better but is just about equal in cost to stainless. For home it’s worth it to invest in good stainless.
Some specific health concerns… If you are sensitive to nickel then you may need to avoid stainless. If you have hemochromatosis then avoid cast iron.
Every kitchen should, IMO, have:
Clad Non-stick fry pan or skillet. Fry pans are slightly shallower than skillets, otherwise they are largely the same.
Clad stainless steel fry pan or skillet.
Disk bottom small and medium sauce pans. 1-1.5qt and 2-3qt
Disk bottom stock pot.
Disk bottom sauté pan.
Steel Fry Pan – Once seasoned these are ideal for pan frying, braising, and other tasks. If you want a good fond then you need a good steel fry pan as it’s the only way to get it.
Lodge cast iron Dutch Oven.
Pizza stone or steel
Cast iron skillet
Beyond this it depends on what you cook and for how many. We have numerous 2 qt stainless sauce pans (Cuisinart & Volrath) for instance along with a colorful variety of other things like Poffertjespans.
Sometimes it’s worth it to get specific products either for quality or value.
Volrath Intrigue is my personal favorite for most stuff as it has very even heat across the bottom. This is also probably the most popular stainless in better restaurants. Many people don’t like the round industrial handles though they’ve recently changed these.
Volrath Tribute tri-ply for non-stick fry pans.
Cuisinart Chef’s Classic is our go to for a lot of things. Less expensive than Volrath, nearly as good for evenness, lighter, more comfortable/gripplable handle and better than other consumer stuff including the very well marketed All-Clad. A step up from Cuisinart might be Fissler or Demeyere and if money were no object we might go there but for 1/4 the cost we’re happy with Cuisinart.
Matfer Bourgeat Black Carbon Steel Fry Pans or de Buyer from bakingsteel.com
Pizzacraft Thermobond Pizza Stone or Baking Steel from bakingsteel.com
* A good way to test evenness is to dust a pan with a light even coat of flour and then heat it up. All of the flour should brown evenly.