I agree that a mixed bag will give you better results. For frying pans, Like AllenMi, I like cast iron. It'll give you great results for all of your frying and saute'ing needs. It is also bulletproof (very durable), and if the seasoning is messed up, it is easily repaired by re-seasoning. It goes from the stove-top to the oven with ease and is versatile enough to fry chicken, bake pizza, simmer a pot roast, and fry eggs. I even use mine occasionally to boil spaghetti in.
Stainless steel saucepans are a must. Get pans with features you will use, such as encapsulated disk bottoms to distribute heat evenly, tight fitting lids, maybe a double-boiler attachment. Get sizes that will allow you to make small batches for such things as cheese sauce or gravies. Get another pan to make family-sized one-pot meals, like soups, stews, etc. And get a stainless stock pot. Another great cooking vessel is the pressure cooker. They come in various levels of price, ranging from about $30 to better than $100. When you learn to use them properly, they greatly shorten cooking time.
This advice is my opinion, and should be taken as such. Your cooking needs and wants may be sustantially different than mine. But a few good cast iorn pans, maybe an eight-inch stainless pan, and some good pots will serve you well for most of you cooking needs. Of course, over time, as your cooking skills grow, you will want to add specialty pans, like a good roasting pan, that can maybe work for making lasagna as well.
Great cookwear doesn't have to cost $1200 per set. You can find great stuff at yard and estate sales. And remember, if you really had to, you can boil water in a paper cup. We did it in boy scouts, over a bed of glowing embers.
A guy who used to be on a previous site that I enjoyed used to close all of his replies with something to this effect, paraphased due to my imperfect memory; What goes into the pot is far more important than is the pot.
Seeeeeeeya; Goodweed of the North