Finishing what I started to say; Griswold, followd by Wagner, then Lodge for cast iron. I would recomend sizes 8 inch, 0, inch, and a 2 inch with high sides for frying chicken, or deep fried foods.
For high carbon steel, or mineral steel, there are some great French makers. They work like cast iron, and need seasoning. When properly seasoned, like cast iron, they are nearly shick-free. And like cast iron, they suffer from hot spots. Unlike cast iron, they won't shatter due to extreme thermal shock. Both cast iron, and mineral steel are oven safe, if they have metal handles.
Eenamled cast iron is great, but will have foods stck if used improperly. They can be hard to clean.
Stainless Steel - Try-ply such as all clad is cream of the crop here. But a good 18/10 stainless with an encapsulated bottom is much less expensive and will give very good service. Just be sure that with stainless, you preheat the pan dry, then add a little oil, and spread it around, then add the food. This makes the pan vertually stick-free. If you don't do this, foods can stick ferociously to SS pans and pots.
Many professional kitchens use bare aluminum pans for their durability, and light weight. Unknown to most people, aluminum pans should be seasoned just as you would season a Cast Iron pan. The seasoning prevents acidic, or alkali foods from reacting with the aluminum, and makes the pans as slippery as their ferrous cousins.
Dutch oven - enameled cast iron, or stainless steel. Must have a good, tight-fitting lid.
Finally, a non-stick, either Teflon, or ceramic pan is a must for French omelets, and eggs, and even crepe;s. Choose thick aluminum to prevent warping. Calpholon is a good brand here, and the anodized outside helps to keep them lookng good.
Pan types that every kitchen should have:
Skillets - in sizes mentioned under cast iron anove
Saucier - in SS, or noon-stick ceramic
8 inch frying pan with sloping sides
stock pot with doulble boiler and steamer
High Carbon Steel latge flat-bottomed wok with helper handle
Any and all pots, and pans should have tight fitting lids. With cast iron, and high carbon steel, the lids must be seasoned, just as you do the pans. Otherwise the steam from foods, coupled with the heat, will cause the lids to rust, and drip rusty water into the food. It won't hurt you, but won't help the food flavor, or how it looks. When seasoned properly, the lids won't corrode and affect the food.
If using in the oven, lid and pan handles need to be oven safte to at least 450'f.
Oh, and don't forget a good roasting pan, with a rack for ribs, chicken, turkey, etc. One large pan will serve to make all of thise, as well as a great pan full of lasagna, manicottie, baked spaghettie, or even a batch of baked beans. I have a large, rectangular 18/10 lasagna pan that is large enough to roast a 22 lb. turkey in, with a rack to hold the bird off of the pan bottom. I use it for all kinds of things. Unfortunately, iti doesn't have a lid. Heavy-duty aluminum foil works to seal everything in though. I can even use it as an indoor smoker in a pinch.
A wonderful way to preare your pots and pans for use over a camp fire - rirst, don't cook over flame, but over a bed of coals, using large pieces of wood, or a metal rgate to hold the pot over the coals. Rub a neutral soap, such as Ivory bar soap all over the outside of the pot, just like coloring it with a crayon. When clean up time comes, the soot comes right off with the soap. Just be careful not to get any of the soap inside the pot, or pan. It won't do any coog thing for the food taste
Hope that gives everyone everything they need.
Oh, one more thing, microwave safe cookwear is something every kitchen should have, for making those quick soups, meals, or deserts in the microwave oven. And of course, there are specialty pans such as egg poaching pans and such. I won one that cooks foour poached ( actually steamed) eggs in butter that are sublime. But then, a properly poached egg in salted water, in an ordinary sauce pan is sublime too, just not as fancy looking.
HHigh quality spring form pans are needed for elegant cheesecakes and cakes. They can be had in circular, and square shapes, and different sizes. For these, quality is key. Kaiser, from Germany, is a great quality spring-form pan. Wilton also makes great baking pans of all types.
If purchasing any glass cookware, for the oven, or stove top, look for boro-silicate glass. It won't shatter over direct flame, under a broiler, and can be used in the fridge to oven, or oven to fridge without shattering.
The old Visions brand of stove-top cookware was boro-silicate glass, and would withstand temps that would melt aluminum cookware. Nut food did stick to it. This is the type of glass used by chemists over direct alcohol flames in test tubes, and beakers. it is completely inert, and non-reactive for all food types.
Seeeeeya; Chief Longwind of the North