I'll agree with the others on don't buy a set. I got by for years with only a hand-me down pot & skillet. (and then got a hand-me down set when my uncle died). If you don't manage to get a lot of stuff at once, you can slowly build up your own set, selecting the pieces that you'd actually use. ... or go to lots of estate auctions and yard sales to build your collection (which my mom still does, as she likes old cast iron).
Take a consideration of what you like to cook, how many people you're cooking for, and the size of your stove & oven.
For instance, I lived alone, and at most I'd cook for a second person at any time, and I had a rather small stove ... so there was no way that I'd have wanted a 12" pan. I started with an 8" and moved up to a 10" after a couple of years. If you tend to do more asian cuisines, you might want instead to use a wok (or flat bottomed wok if on an electric stove, or just a skillet to be more versatile)
If you come from more of a pasta background, you'd likely want a larger pot than you'd want if you tend to cook rice-based cuisines.
As for materials, if you're used to cooking with non-stick, I'd keep doing that. If you're used to cooking on stainless steel, or cast-iron, just stick with what you're familiar with.
The TV show America's Test Kitchen does review of tools, and although All-clad tends to win their rounds of testing for stainless, they also designate a 'reasonably priced alternative'. I've never signed up for their website, so I don't know if they describe their testing methodology on there (so you can see what they thought were important considerations), and if they detail what the drawbacks of the various items tested were.
The only one caveat I would make is that for stainless steel, you really need to look into its construction. Stainless on its own is a poor heat conductor, so you need to look to what the proportion (if any) aluminum or copper is used. For years I used (and still use some pieces of) Revereware and also have a few pieces of Tools of the Trade, both of which have a disk of aluminum on the bottom. Some use copper disks (even better conductor), and others like All-clad have it, but it's then encased in stainless, so it's harder to tell how much just by looking at it.
(and similar comments on other bits ... I didn't have much of anything else other than utensils, knives and a cutting board. My pot would double as a mixing bowl, and I'd use the lid on the pot in place of a strainer)