As Chef Tod said, two chefs = five opinions.
First, have some perspective: Once you get up from the level of bad to good -- you're not going to get a lot of help or hindrance from a pan. Great pans won't make you a good cook or your food any better than excellent or very good pans. You're balancing comfort and appearance even more than performance.
And appearance counts for a lot. Pots and pans are a part of your life, and you might as well enjoy the way yours (pots and pans, not lives) look.
Also, there are a number of good materials -- each with its own advantages. If I could have a fantasy set with an infinite number of skillets, I'd use (non-stainless) carbon steel for most purposes -- even though it doesn't heat as evenly as copper or aluminum, it has other wonderful properties which make up for that. The big problem is that it's reactive (although not highly) and you can't long-cook very acidic foods without affecting flavor and color. "I don't want to go off on a rant, but..." No, I really don't want to waste a lot of time on something that doesn't answer the question, but...
Aluminum is also highly reactive. It has other problems too, like warping. Most home cooks don't want their core set of pans and pots as plain aluminum. For awhile, anodized aluminum was very popular, and I don't really have many criticisms. It was good stuff, as good as anything else in my opinion; and most of my own set is old, anodized Calphalon. It's just not made anymore.
That said, aluminum warps, dents, scratches easily and so on. Restaurant cookware gets treated very harshly -- for instance it sees flames which go well up the sides and completely wreck the exteriors; it gets slammed, misused, abused, dinged, used for improper purposes, and probably used for immoral purposes too. No matter what a restaurant uses, it needes frequent replacement (or repair), and that cost money. For a restaurant, aluminum's primary virture is its price -- cheap. For a pro cook, it's the efficiency and relatively light weight considering its thickness. But for a home cook, it's hard to see a reason for plain aluminum.
Enamel over cast and enamel over steel can be very good pans, too. The problems of expense and weight are secondary compared to the fact that it starts looking crummy and stays that way. If you like stained, you'll like enamel.
Cast iron is too heavy and too slow for most things. It's also highly reactive. On the other hand, the things it's good for it's great for. Nice to have a few pieces.
And at last...
Stainless is not reactive, and it's durable too (as opposed to tin linings, non-stick finishes, and enamel). It's not an ideal pan interior, but none is. For most people, stainless is the best practical pan interior.
Exteriors are another matter.
Good, modern stainless comes in two basic flavors -- disk and multi-ply. With shallow, and other pans used with very little liquid, multi-ply construction really does make a difference; and is clearly superior. Once you get into sauce pans, larger pots, stock pots, and whatnot disks work as well.
Most good multi-ply pans spread the heat as evenly as any other good multi-ply pan. No matter what the number of plies, and what's on the exterior, most use aluminum to do the heavy lifting. If you're paying extra for a copper ply, with very few exceptions, that's what you're doing: Paying extra. Unfortunately, you don't get anything for it.
Lots of layers (like seven) has some advantages over a few layers (like three). It resists warping better, spreads the heat a little more evenly, tends to be a little more responsive, and so on. As a practical matter, these advantages -- other than warping -- tend to be slight.
There are a lot of multi-ply lines that will satisfy your requirements of "good cookware with nice looking handles," including All-Clad, Calphalon, Cook's Essentials, DeMeyere, Mauviel, Viking, etc. It all works pretty much the same. If I were buying stainless tomorrow, I'd buy Vollrath; but you don't like their looks, so don't buy it.
Since looks are important, start there. Look for looks.
Next look for comfortable handles. A lot of people HATE All-Clad handles.
Look for price. All this stuff goes on sale, and you can usually find one brand which is the equal of whatever it was you thought was your first choice for substantially less money.
Weight cuts both ways. Heavier pans are usually better pans, but for women especially, pan weight can be a big negative.
You don't necessarily want a huge set with every pot and pan known to man. It's nice to have a few other pans made form different materials -- or just because you like one maker's 10" saute pan with a helper handle, another's 10" skillet, and another's 2 qt Windsor.
There's a lot to be said for buying from Bed Bath and Beyond or somewhere else with that level of customer service.
Why don't you look around a little, and come back with some specific things you do like. I don't think you're going to get unanimous agreement about any particular line with a questions like "what's best." Everyone swears by what they like, and that's just the way it is. Better if you can ask, "what do you think about this?"
So, what do you think about that?