I would recommend 4 basic pieces:
9" Saute pan, stainless, straight sides.
Omelette pan, aluminum or stainless, w/ non-stick coating.
Sauce pan, 4 - 6 qt. preferably stainless.
Stock pot, 8 - 12 qt., preferably stainless.
Having those basics will allow you to cook nearly any dish. A Dutch oven and a cast iron skillet are nice additions too, but not mandatory for someone just getting started.
If you want to find a good deal on cookware you might want to go to your local Marshall's and check out the clearance section. They often have Emerilware, Calphalon, and sometimes even All-Clad for a very reasonable price.
This is a very good list. Even after years of cooking, 90% of what I use is the following:
3qt chef's pan, hard anodized (a chef's pan has sloping sides)
9" saute, hard anodized
large stock pot
12" skillet, cast iron
For the hard anodized, you don't necessarily need a name brand. Mine are Chef's Catalog Brand, since discontinued. Similar can be found from a restaurant supply or even TJ Maxx, Marshalls, etc, on discount. Make sure it's evenly thick (not just a thick base with thin sides). These are NOT non-stick, but they are stick resistant, and only get better with age.
For a stock pot, cheap is fine. Mine is the kind with a thick bottom and thinner sides.
Cast iron is easy. Lodge pre-seasoned from Amazon is good and cheap.
Beyond this, an enameled cast iron dutch oven is really nice, but I don't have one yet. Le Creuset is the defacto king, but very expensive. A non-stick skillet is good for eggs, omelets, and crepes. Buy a cheapo, like the grocery store kind, or similar. Replace as necessary - seriously, treat it as nearly disposable. Even the most expensive non-stick pans have their coating wear or scratch off, so don't worry about it, get a cheap one, and use all the metal utensils you want on it.
I prefer hard anodized to stainless and non-stick, but that's just a personal thing. I like the even heating of hard anodized and for me the release is a little better than stainless. However, mine are a bit older and very smooth from years of use. Hard anodized is a bit of a bitch when its new, but it will eventually comply.
If you want to use the dishwasher, go stainless. Hard anodized is generally not dishwasher safe. Same for cast iron.