Make a very specific list for all the folks who like to give you a present- brand, size, etc.

Copper or aluminum in the bottom helps them heat more evenly, but is not critical. Oven proof handles, so they can go from stovetop to oven are VERY convenient, especially for the larger pots.

Don't buy a set. For regular family use, I would recommend starting with a 10" and a 12" saute/ frying pan- the new deeper sided ones with the extra handle on the opposite side are great- a 3-4 quart saucepan, and an 8 quart stockpot/ Dutch oven to start. 6 quart is OK too, but 8 is way more flexble.

Check out the sale/clearance bins at the Corning Revere factory outlet, the Farberware outlet, and other kitchenware factory outlets. You have to know what you are looking for, size and brand=wise, but I have found top quality pots as much as 90% off retail this way, sometimes they are lidless, but I have an assortment of glass and other lids I prefer anyway! I have found terrific top quality pots at Ross outlets- especially the housewares clearance, when a lid is lost- and for high end, check out Tuesday Morning outlets. There, I have even found affordable stainless steel cookie sheets and loaf pans a few times, of the $32 each marked down to $7 each variety.

Cuisinart, Farberware, and Revere ware are three widely available reliable stainless steel brands.