Update: I did want to state a very important point, I love cooking hamburgers in a pan so I'm slightly worried that any other pan besides non-stick will make my burger fall apart. They're the frozen pre-made burgers.

I don't know about frozen burgers, but patties made with fresh ground beef cook very nicely in a cast-iron pan.

Unless you will be cooking a lot of stuff....I see no reason for you to need more than a small non stick fry pan...about the size for 2 burgers or a 3 egg omelette, a sauce pan of about 2 quarts....works for veggies potatoes, heating soup and even a small amount of pasta. Then you need a roasting pan of a Dutch oven a baking pan and perhaps a pizza pan and a cookie sheet...
Why do you need a $200 set of cookware? Best use that money for books.
Linda C