One crucial thing to consider is the type of stove you will be using, gas, induction or "plain old" cast iron.
Since I have never myself worked much on gas-stoves I cannot say for sure. But I am told that for gas, coppper is the thing. But only for gas. For induction copper is no-no. For a plain old stove you will need a really flat bottom surface, and copper it perhaps too soft to achieve that after a year or two of use.
Induction places a demand on iron-cores of the cookingwares.
But for a plain old stove I would say that the "cheap non-stick" (or on a gas-stove) is quite alright. As long as the non-stick surface is not too worn.
Personally I have a set of non-stick cooking wares for regular frying (onions, bacon etc). Cast iron skillet for frying a slice of beed. Stainess steel for cooking (pasta, soup and "not easy burn" souses.
/L