The best cookware is that which will keep you safe from contamination from dangerous metals and toxic gases that a lot of standard cookware contains. Good healthy cookware is worth the money you spend for it.
The first thing to replace is any aluminum cookware. I remember my grandmother (and even my mother) using aluminum pots, pans, pie plates, and baking dishes all the time. They were lightweight and conducted heat well. Unfortunately they also have been found to release small amounts of the metal into the body, especially when acidic foods are cooked in them.
This can lead to all sorts of health problems, including anemia, decreased liver function, poor coordination, calcium deficiency and memory loss. It has also been associated with Alzheimer's disease, as many people who died with Alzheimer's were found to have had excessive amounts of aluminum in their brains.
Next, get rid of all your non-stick pans. Now before you protest that you'll never be able to successfully cook a fried egg again without breaking the yolk, you should be aware that non-stick pans such as Teflon release a toxic gas called PFOA (perfluorinated chemicals) when they are heated above 500°F. And when the pan is heated further to 680°F, it releases at least six more toxic gases.
PFOAs have been shown to cause a whole host of health problems, including infertility, damage to the pituitary, an increase in tumors and prostate cancer.
So what are the alternatives?
The best cookware to use depends to some extent on what you are cooking.
The best all-around healthy cookware in my opinion is castiron cookware. It is safe, has a non-stick surface if seasoned properly, and is relatively affordable. The best cast iron cookware can withstand high temperatures and distributes the heat evenly throughout the pan.
I have had my Lodge cast iron cookware for 20 years now, and it only gets better with time. I can fry an egg to perfection, with no broken yolks due to sticking to the pan, and it gives my pancakes a beautiful golden color.
Cast iron heats your food evenly and provides trace amounts of iron to your diet. It is heavy though, so if you have difficulty lifting heavy objects you may need to choose another form of healthy cookware. It also is not good for cooking with acidic foods such as tomatoes (tomato sauce for instance), lemon juice, vinegar, or wine. It will create a metallic taste in the food.
In these cases you should consider either enameled cast iron cookware, high-quality stainless steel cookware, or ceramic cookware.
Enameled cast iron is healthy cookware great for anything that has to go from stovetop to oven. It works well in contact with an open flame and its metal handles are oven-friendly (assuming all parts of your cookware are made of metal). And the enameled surface will ensure acidic foods will not react with it. Its drawback is that it tends to be very expensive, but if you can afford at least one or two pieces I think you will find them worth it!
Glazed earthenware and ceramic cookware can also be excellent for baking, though find out from the manufacturer if their glaze is free of lead and cadmium. Some earthenware, particularly from Mexico and China, has been found to leach lead. A reputable manufacturer should ensure their product has been tested and found to be free from leachable heavy metals.
An investment in healthy cookware is as important to your diet as making healthy food choices. But a few pieces of the best quality cookware you can afford and it will serve you well for many years.