I've developed a specific approach to painting metallic surfaces over years of trying various techniques, and the framework I landed on is simple enough to be reliably repeatable.

Metals are classified by their reflectivity profile: polished metals (chrome, mirror-finish steel) reflect almost everything they see. Brushed or matte metals (brushed steel, pewter) reflect a blurred version of the environment. Oxidized or patinated metals (copper, bronze, rust) absorb more and reflect less.

For polished metals: identify the most significant things in the environment the metal is reflecting and paint simplified, high-contrast versions of them. The ground plane reflection is almost always visible. The sky reflection occupies the top half of curved surfaces.

For brushed metals: everything polished metals do, but with heavy horizontal blur following the brushing direction.

For patinated metals: the surface texture is the dominant visual element. Greens and oranges for copper oxidation, warm browns and greys for rust. The reflectivity is low — treat it more like a matte painted surface.