Cookware

Stainless steel
For most people, stainless steel cookware is the most versatile and overall best material for the majority of cooking because it combines a durable and non-reactive cooking surface with good heat distribution and responsiveness.

Stainless cookware always incorporates a more conductive material like aluminum or (more rarely) copper, but the cooking surface itself is stainless steel. Unlike just about every other cooking surface, stainless is both non-reactive (so you can cook acidic stuff in it for as long as you want) and okay to use metal utensils on. You'd have to try pretty hard to ruin a good-quality stainless pan, so they don't require any babying.

The big downside of stainless is that it's not nonstick. This means you probably don't want to cook things like eggs or pancakes in one of these. However, with proper technique most proteins will naturally release and will leave behind fond, which can be turned into a delicious pan sauce. For most cooking tasks, sticking shouldn't be a big concern with stainless.

Stainless also tends to be relatively expensive, especially for the good stuff. For top-quality stuff, you should expect to pay US$100+ per piece. However, keep in mind that this stuff should last you a lifetime.

Fully clad vs. disk bottoms
There are two general types of stainless steel pans

Cast iron and carbon steel
Cast iron especially has a bit of a cult following, but both of these materials act similarly. They're not terribly conductive (meaning they're not great at reacting to changes in stove temp or at distributing heat evenly) but they have high thermal mass, meaning that the pan will stay hot even when you throw a giant cut of chilled steak into it. The biggest advantage though is that these durable pans develop a long-lasting layer of non-stick seasoning with use. A seasoned cast iron or carbon steel pan isn't as nonstick as an actual nonstick pan, but it's plenty nonstick for most tasks.

Seasoning isn't only to make these pans nonstick: it also protects them from rusting. In addition to being susceptible to rust, both materials are reactive with acids. Cooking acidic foods (e.g. tomato sauce) in either for a long time may strip the seasoning from the pan and leave the food with a metallic taste.

Differences between cast iron and carbon steel
In terms of the thermal properties of the material itself, it isn't really worth distinguishing cast iron and carbon steel. The big difference isn't the material itself, but rather the kinds of pans that are generally made out of each.

Cast iron pans are generally pretty straight-sided. The most popular brand, Lodge, is very affordable and has a slightly pebbled surface as a result of the casting process. Lodge pans, and most cast iron, come pre-seasoned, so you don't need to do much to start enjoying the nonstick surface. Some more expensive or vintage cast iron pans have smooth surfaces, which some people think make them more nonstick.

The sides of carbon steel pans tend to be much more dramatically sloped. This makes it easier to toss food but also reduces the size of the cooking surface. Big makers of carbon steel pans include de Buyer and Matfer Bourgeat. Their pans are roughly twice the price of Lodge cast iron and have smooth surfaces that do not come seasoned, meaning you'll need to season them yourself before they're truly nonstick. High quality carbon steel pans are usually a bit thinner than cast iron pans, which it turn makes them a bit lighter. However, carbon steel is still by no means light.

Overall, there isn't much reason to pay more for carbon steel, especially since you need to go through the hassle of seasoning it yourself.