Non-stick issue: Most folks that are really into cooking (but not necessarily gourmet or professional) claim that everyone needs at least 1 non-stick fry pan for cooking eggs or dishes with eggs in them. BUT they almost uniformly caution against using non-stick for everything else, as you just cannot get the same browning performance as you can with regular pans. Then there is the potential peeling issue. Lastly, non-stick pans are not supposed to be placed under the broiler - they cannot tolerate the higher heat. This is a big disadvantage, since so many cooking techniques call for starting something on the stove and finishing it under the broiler. I do this all the time, especially for seafood and fillet mignon.
-Set versus individual pieces issue: While I completely agree that there may not be one entire set that will do everything well, I do believe that one can't go wrong with buying a basic set of something that you like and then supplementing that with other pieces from the same or entirely different lines down the road. It is a cost effective way to shop for cookware, IMHO. I started out with a 10-piece set of All Clad stainless and since then, have added about 12 more pieces of AC, plus 12 pieces of Le Creuset enameled cast iron (another terrific product).
-Does appearance matter? Will the pots be on display? If so, you might want to consider something in a stainless steel finish, like All Clad. I have had my set of AC stainless (Al core for conductivity; SS for appearance and ease of cleaning) for 6 years now and they still look and perform as if they had never been used. The stay cool handles are nice, plus they go in the dishwasher. As to the glass lids issue, I love the way they look but chose not to get any, as our floors are tile and I worried about breakage. I suppose replacements are available, but what about 20 years from now?
Are you using gas or electric? If electric, is it a coil top or glass/smoothtop? If the latter, then there are other considerations as well. (You cannot use anthing that has copper on the OUTSIDE of the bottom; cannot use glass cookware, such as Visions by Corning; must use only pots that are metal, smooth and 100% flat on the bottom, which eliminates Circulon...)