1) Tri ply is the safest bet, because the aluminum goes up the sides. This prevents food from sticking or burning on the sides. If you're going to buy a complete set, I'd get the tri-ply.

2)Some of these stainless sets have "encapsulated disc bottoms" - I would avoid these as a set, because while the bottoms are good, the sides are much worse(it's stainless only-that tends to burn or sizzle liquids). Now, for a very shallow, non-stick egg pan/pancake pan, these disc bottoms work well. Or if you need a very large stock pot for soups, then the stainless encapsulated disc is also O.K.(don't get non-stick in a stock pot).. But disc bottoms make lousy sauce pans or fry/saute pans, because the sides burn food.

3) "Copper band"- this Sear's set looks like an "encapsulated disc" and therefore I'd avoid it as a set.
The copper is made to 'look' thicker than it really is.

4) Tri-ply Copper is out there- several companies sell it- it's about as good as regular stainless/alum/stainless tri-ply, but looks nice when new- the copper is harder to keep looking nice though, and is too thin to really make a difference in cooking.

5)Avoid the all-aluminum pans (with or without an anodized finish) - they cook well, but tend to warp when thin and react to tomato sauce if scratched. However, thicker, with an anodized surface is better (anodized is not the same as non-stick) if you do get it. It may scratch, and not like it if you overheat it, but it cooks great. Instead of anodized, consider---
Aluminum, but with a thin layer of stainless on the inside (very good), just make sure the aluminum is on the WHOLE pan (including sides).. This is sort of rare, but it's good because the aluminum is thicker than tri-ply and you still have the inner stainless that is non-reactive and will keep it from warping.

6)There are 5-7 ply cookware. This stuff is also very good, but very expensive.

7) Thick copper with stainless on the inside is maybe the best, but extremely expensive-heavy, and hard to keep looking nice- must be hand washed.

I'd recommend the tri-ply set (do not get non-stick) and then if you need a single, non-stick egg pan, getting one with a disc bottom is ok., or a tri-ply. Also, a cast iron fry pan and a porcelain (colored) cast-iron dutch oven (casserole) makes a good addition.