Welcome MFK (excellent initials for a culinary person!).
Read
Understanding Stovetop Cookware on eGullet. It is incredibly useful for understanding the properties and uses for different pots, pans, and materials.
My advice is:
Figure out how much you want to spend first. For some pans, more money does mean better quality.
Think about what you cook and then think about the best pots and pans for the job. There are a lot of pots and pans out there that you won't use that often, or at all. So why get them -or why get the best quality version of them. Also think about how you cook. Do you use high heat a lot? Cheaper saute pans are more likely to buckle.
For some pots and pans it is worth spending more money to get the best quality. For example, if you'll use a straight-sided saute pan, invest a lot in a good one. For other pots and pans, it makes more sense to buy a middle of the road version. This is true for things that you won't use that often, as I noted above. It is also true for things like roasting pans and non-stick skillets. There is very little performance benefit to having a clad (i.e. different materials, such as aluminum and stainless steel, pressed together) roasting pan compared to a 100 percent stainless steel pan, yet the clad pan will be 2-3 times as expensive. For non-stick pans, the non-stick surface will begin to scratch over time, even if you are careful. Then you'll have to replace the pan. So getting an All-clad stainless steel pan in which the bottom lasts a lifetime, but the top doesn't, is not a great idea. I get $30 Vollrath non-stick pans from Northwestern Cutlery.
You asked about copper pans lined with stainless steel. This is a good example of why you need to start by thinking about what you cook and then pick the best tool. From Understanding Stovetop Cookware:
Copper with an Interior Lining of Stainless Steel
- Copper has the best overall thermal properties for most cooking tasks. It has excellent thermal conductivity and a high specific heat per cubic centimeter. This means that it provides extremely even heat, is very responsive and holds a lot of heat without needing to be all that thick. However, the thermal conductivity is so fast that copper pans not retain heat well once off the heat -- this is the converse of responsiveness.
...
- Common uses: Almost every pan in the kitchen is manufactured in this design. Especially useful for cooking tasks that require the ultimate in heat control (e.g., making delicate temperature-sensitive sauces) or those where it is particularly beneficial to take advantage of copper’s ability to conduct a lot of heat all the way up the sides of the cooking vessel (e.g., reductions). This design does not have any particular advantages for heating large volumes of thin liquids in stock pots, rondeaux, casseroles, etc.
- Representative manufacturers: Bourgeat, Falk Culinair, Mauviel.
So, if you make fried chicken a lot, you are better off with a $20 cast iron pan.
Most people will say you should avoid sets. The reason for this is that you'll probably pay for pans you won't use and/or that you don't need the same quality level for each pan. Having said that, sometimes you can get excellent deals on sets. So don't dismiss them out of hand. Also, the exact contents of All-Clad sets differs from retailer to retailer.
I presume you are referring to the Cooks Illustrated article. They didn't like the expensive Mauvel because of the handle and other design issues. I tend to agree with a lot of their opinions, but do note that they sometimes have quirky views. In this case, the large saucepan is simply the wrong pan for making a pastry cream, so some of their design criticisms are perhaps not that important.