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I will agree with Steve, you need pans with a flat bottom. The heavier the bottom of the pan, the more it resists warping. This also makes the pan less likely to burn, although if you do get the pan screaming hot, it will take longer to cool down.
I'm not sure how durable a surface Corian is. My other half keeps mentioning that she wants a glass-top stove, but I'm scared I'll shatter the glass, as I do a lot of shaking/flipping in the course of cooking. I also tend to let a cast-iron skillet bounce a little bit in the course of setting it on a burner.
I have a bunch of Cast-iron skillets and a few pieces of All-Clad and Caphalon. The All-Clad and Caphalon are all tri-ply stainless/aluminum/stainless. I have not had any issues with warping in the years I've had those pans, although I've noticed a few small impact marks, with a corresponding small dent on the other side.
One thing to watch out for with older cast-iron skillets, is that some of them have a "heat ring" on the bottom. This is a raised ridge that runs along the outer edge of the bottom of the pan. It serves to catch the heat from a gas burner. It will work on an electric element, provided the pan is big enough that the burner fits up inside the heat ring and makes contact with the bottom of the pan. Lodge cast-iron, at least the contemporary stuff, does not have a heat ring
All my skillets at home are cast-iron, with a few being cheap aluminum with non-stick interiors that I use for omelets/eggs. If you go with stainless steel, be sure to let the pan heat up first, then add the oil/fat, then the food to be cooked. If you have issues with staining, get some Weenol or Bar Keeper's Friend. I just let the pan soak with warm water over a burner at it's lowest setting, then attack the food residue with a green scrubbie. For a really bad one, caked-on, baked-on, i.e., SCORCHED food, a steel wool pad works wonders, but I am careful with those.
Le Crueset makes a NICE enameled cast-iron skillet, at least they did 12 years ago. I haven't looked at any of those. I wouldn't use metal utensils in those, as you could chip the enamel off.
Hopefully that answers your questions. If you have any more, feel free to ask.
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