Your cookware should be fine for almost every use. Do not use high heat after bringing the contents to the boiling point, if at all. One thing you might want to invest in is a good enamel stew pot for cooking acid foods like tomato based stews, soups and pasta sauces. From what I have read, acidic food tends to make cookware leach metal more than any other food. Also, be sure and not store your food in the cookware.
I learned to cook with my mother's heavy duty aluminum pots and pans and has taken a long time to get used to other kinds of cookware. I tended to scorch a lot of food I never scorched before. One of the best things I ever bought was an electric vegetable and rice steamer. It makes the veggies delicious and cooked to perfection every time.