Not sure how much you want to go into the research... if you're really into it you may want to read this:
I don't believe copper will add much more than a pretty color to your cookware. If that's important for you aesthetically then go for it, otherwise you can pass.
Stainless steel is ok, it's not non-stick but it's pretty easy to use, pretty easy to clean, and can handle high temps. I personally went for the Calphalon pans because of the shape of the handle, and I'm really happy with them.
Carbon steel is great, but it requires a bit more tender love and care to maintain than stainless steel. You'll have to season it before you use it, you'll have to avoid using them with high acid food such as tomatoes or wine, you'll have to keep them dry to avoid rust, etc... the pros are, you can make them virtually non-stick and at the same time use them to develop a fond. They obviously can handle the heat, but you'll need a towel to handle them.
Cast iron is great for the same reasons, but is heavier.
Non-stick... they have all sorts of non-stick pans nowadays, and I believe pros use a LOT of them, much more than they'd lead you to believe. Some of them are very good, I'm just not sure how long they can last, which is why I personally choose to use stainless steel or carbon steel: the pans last forever.
Aluminum is light, cheap and great for the heat, not so good because of how it reacts with acid.
Some really good brands are Matfer Bourgeat and Vollrath.