My Opinions on starter cookware:
First of all, most beginner cooks focus too much on non-stick. The only thing you need to be non-stick is one pan to cook really sticky things (like fried eggs) in. For that one I'm actually a fan of cast iron. You don't mention exactly what type of pans you have here, so I'm going to lay out my overall recommendations.
A couple of definitions, though:
A "stockpot" is a large cooking vessel that doesn't have a long handle on it.
A "saucepan" is a smaller high-walled pan with a long handle.
A "skillet" is a low-walled pan with a long handle.
A "Dutch Oven" is a very deep, heavy, cast iron pot.
- An enameled cast iron Dutch oven. You can use this to make stews in, for things you simmer a long time, and I love to bake bread in mine. You can get this Lodge for about $70. Lodge Dutch Oven
- A non-stick skillet. This is used for cooking really sticky things. If you get a cast-iron skillet for this, as a I recommend, you can also use it for cooking all sorts of other things (I regularly use mine for bacon, Chicago deep-dish pizza, and baking cornbread in, for example). The 12" Lodge one is about $32: Lodge Skillet If you decide to go non-stick, I have no specific advice because I don't use it.
- Stainless steel for everything else. It's indestructible, easy to clean, and a lot more versatile than the alternatives. Elsewhere in the thread I've seen All-Clad recommended, and it's great stuff, but if you have a $200 budget you should buy much cheaper stuff. You can get stuff that performs just fine for much much less. Most of the value of All-Clad is aesthetic (look and feel) versus practical - you're paying many multiples of cost for maybe 20% better performance. If you can afford it, go for it (I have an extensive collection) but you can get perfectly adequate for much less money. You need at a bare minimum, a large stockpot (something like 12 quarts) for boiling pasta and making soups, two smaller saucepans for cooking almost anything that needs boiling (say 2 and 4 quarts), and a large stainless steel skillet (12") that you do almost all your high-heat cooking in. This Vollrath set I think is an especial bargain. If the pans you mention above are nonstick, I'd recommend just buying the whole thing. But, if not, the pieces of it are individually available. There's a substantial discount for buying the whole thing, so much that it might cheaper to buy the set and then donate what you don't need.
- Vollrath Set about $95
- Vollrath Stockpot $55
- Vollrath 1 qt. saucepan $35
- Vollrath 2 3/4 qt saucepan $45
- Vollrath 12 1/2" skillet $55
So there you go. Dutch Oven for $70, cast-iron skillet for $32, stainless steel set for $95, all in it's $197 (plus shipping, but if you want to poke around you can probably find the Lodge stuff locally at camping-supply stores and you might be able to find the Vollrath stuff at a local restaurant-supply store (which are open to the public if you don't know, and generally a great place to get really serviceable kitchen gear)).