I heard silicone utensils aren't safe. Is it best to use melamine or silicone on nonstick cookware?

Any of the above. When did silicone become unsafe? Overheat melamine and you get toxins forming in the partially combusted or pyrolized material from which it's made. (Any melamine discolored from exposure to heat is best discarded.) Overheat silicone and you get silicone. Replace any utensil that has been heat damaged to remove any doubts. Any of the products will work well if the manufacturers' instructions are followed. Don't have them handy? Use common sense. Or WikiAnswers. Bon appétit.