I understand your position, and believe I can reconcile the answers so everything not only makes sense, but you can give your friends a meaningful answer regarding the cookset.
There are a variety of different types of cookware including carbon-steel, enamel over cast iron, cast iron, multiple-ply stainless, non-stick on stainless, non-stick on aluminum, stainless in anodized aluminum, plain aluminum etc.
Some people are very happy with one or several of the many forms of non-stick. Good cooks, generally are not. On the plus side, non-stick is easy to clean. The fact that food doesn't stick is usually not a good thing. A good cook using decent cookware can keep most foods from sticking just by cooking them properly. Even the best non-stick is somewhat fragile and when it starts to chip and peel, the pot must be tossed.
That said, you can combine all the good advice you're getting by having your friends buy you a nice set of cookware with a decent assortment of sizes, then adding your own special purpose pieces, such as a dedicated omelette pan, a chicken-fryer, and so forth, as your cooking horizons expand.
Stainless steel interiors are probably the most practical for a "set." Stainless is not reactive, and cleans fairly easily. Where was I? Oh yes, practical because it's not reactive and cleans easily. It's not truly non-stick but you keep food from sticking by preheating the pan, adding an appropriate amount of oil, preheating the oil before adding the food, and not trying to move or turn the food until it's ready.
Old fashioned stainless had a lot of problems that modern, multiple ply construction has pretty much solved. While there are other construction solutions, multiple ply is probably the most common in high-end residential cookware. Multiple ply means the interior is stainless; with some lines the exterior will be another material -- usually aluminum, or the exterior will be stainless with an aluminum inner core.
It's the All Clad stainless-aluminum-stainless sandwich you probably heard complaints about. That is, the exteriors can pretty crummy -- especially if the flame is so high it wraps around the side. However, this ins't a big deal really. It can be cleaned very easily with oven cleaner.
The choice of exterior -- aluminum, anodized (dark grey) aluminum or stainless is really an aesthetic choice. There isn't much performance difference -- certainly not enough to worry about.
The current "hot lines" are All-Clad MC2, All-Clad Stainless, Calphalon Tri-Ply and Gourmet Standard Tri-Ply. There are a few others worth looking at if none of these tickle your fancy. Your best bet is for the two of you to find a store and handle a few of the pans to get a sense of their weight and how their handles feel. In fact, other than cosmetics, "feel" is the major difference. Performance is essentially equal.
Since someone else is paying for this -- and price is no object, I suggest asking for the set which includes the "Spaghetti Pot." That's a large stock pot with a spaghetti strainer/steamer plus smaller steamer insert. It should come with four other sauce pans and at least two, but preferably three frying pans (8", 10" and 12"), as well as a bunch of lids. Unless you're both big and strong, you'll want a helper-handle on the 12" frying pan (which will have straight sides and be called a "saute pan").
All in all you're probably looking at something like 14 pieces and some serious change. This is the sort of ambitious and wonderful present your friends will be proud to give and will serve you in good stead for decades. Get it, use it, love it. That doesn't mean it's the be all and end all of cookware or that you'll never want another pan or pot. Just that you're off to a great start.
Best wishes and congratulations as appropriate. Good luck to the both of you,