Cast iron cookware has many virtues. I'm not the first to point them out. But I'm going to point them out anyway.
- Cast iron heats uniformly. Great for searing, toasting, and sautéeing, and great for baking.
- It holds a lot of heat. So when you drop in a cold piece of something, the pan doesn't get cold, and the something sears. Or if the pan is full of oil, the oil doesn't get cold.
- You can make cast iron REALLY hot. Simply put it on a high flame with nothing in it for a while. Great for searing and blackening. Cast iron can also go in the oven, and under the broiler if you are sensible about it.
- Over time and with proper use, cast iron develops a pretty good non-stick surface. The more you fry in it, the better it cooks, the less it sticks, and the easier it gets to clean.
- It is heavy, and will impress your guests and potential burglars.
- It is nearly indestructible. You can use metal spoons and tongs in it all day long. Even if you mess up its finish, you can easily refinish it yourself.
- It is a bargain, whether you buy it new or used.
- If you use it to cook things that are acidic or too liquid (spinach, tomatoes, stews, soups), it can oxidize, discoloring the food, and adding some iron to it. A little supplemental iron in our diets can be okay, depending, but black tomato sauce is a bummer.
- Cast iron holds a lot of heat. If you want to be able to vary the temperature quickly, like when you're stir-frying or sautéeing something delicate, this can be a drawback.
Enameled cast iron cooks very much like cast iron, except that its finish is impervious to acid and liquid. It is more fragile than cast iron; you don't want to bang it with a metal spoon, or burn things in it. It tends to be expensive. Great for soups, stews, and roasting.
Anodized aluminum heats nicely. Unlike cast iron, aluminum holds little heat; this can be nice when you want to vary the heat quickly and precisely. Anodized aluminum is also more fragile than cast iron, is expensive, and is increasingly hard to find. Anodized aluminum can really do everything pretty well; if I could only have one type of pan, this might be it. Fortunately, I have no such limitation.
Unfinished aluminum has nothing to recommend it over anodized aluminum, except that it's cheap. But unfinished aluminum oxidizes, and is pretty toxic, so I don't use it.
Stainless steel heats okay but not great, although some fancy stainless pans, like All-Clad and other laminated types, heat nicely. Stainless steel is impervious to acid and liquid, is not so fragile, and can be inexpensive (although not the All-Clad). A good choice for messy, sticky, or corrosive things, like dessert sauces and acidic reductions. Or for boiling water.
Non-stick is fragile, and can't safely be used on high heat because of toxicity. I can see the case for frying eggs and fish in non-stick, because fried eggs and fish are very delicate—but that's about all. I avoid it when I have a choice.
I don't have experience with glass cookware. My impression is that it heats poorly, is fragile, and is difficult to clean.