The “best” set of pans for a home cook are the ones that work best for you. There are some basic considerations.
Aluminum non-stick pans – These break down between metal-ceramic coated and regular (mostly petroleum-based) coated. For most cooking, the metal-ceramic coated pans are the best choice, with coatings like Thermalon. These pans almost all specify that they are metal utensil safe. But these pans are very, very slick, and for some cooking, especially meats, you do want some level of tooth. The regular coated pans often have a surface with enough grain to provide a good tooth for browning meats. The regular coated pans generally specify that they are not metal utensil safe, but some specify they are metal utensil safe. It is just a good idea not to use metal utensils for scraping and cutting in the pan.
Stainless Steel 3–ply pans – These are made with magnetic stainless on the outside and food-grade stainless on the inside, with layers of aluminum sandwiched in between to improve heat conduction. Ensure they are three-ply (or more) and not just a single layer of stainless steel. Make sure that the handles are not wood or plastic, which can be a problem when you want to use the pans in the oven or under the broiler. Some of these pans come with all stainless lids, but most have glass lids with handles.
Cast Iron (regular and porcelain-coated) – These usually break down into traditional cast iron like Lodge, all one piece, including handles. In most cases, the pans must be seasoned to work as intended, especially with meats and eggs. There are lots of good instructions on how to use them that I won’t go into here. Just make sure that the walls are fairly heavy. Heavy is the keyword. The pans are heavy, too heavy for many children and older cooks. But they do a great job and, if correctly used, should last for a lifetime, and even your kids’ lifetime. Whenever they do not work as intended, it’s time to cook them out and re-season them. The porcelain-coated pans, like the classic Le Creuset from France, will also last a lifetime, are quite good at being non-stick, come in bright colors, and can be used in almost any cooking.
Carbon Steel pans – Carbon steel pans have been around for a long time, but they are fairly new to most cooks. They need to be seasoned like cast iron pans, but they are lighter and easier to care for. The handles are similar to stainless pans, not cast in like cast iron. They may look a little bedraggled from constant use, but that does not affect their ability to cook with them. I always suggest, just like all pots and pans, that they are washed by hand, but make sure that they are well dried or even wiped with a cloth with some olive oil to protect against rust. In my opinion, they will cook well if you are experienced, but they are more difficult to care for and cook with than 3-ply stainless pans.