I am of the mind that any kind of gold and any color gemstone can look fabulous on any color and texture of skin. However, there is no denying that certain gems really sparkle when they meet their perfect skin tone.
Warm
You have yellow or peach tones in your skin, and golden or red tones in your hair. Your veins appear greenish
Best Metals: Yellow gold, high purity gold (22k, 24k), rose gold, copper
Best Gems: Turquoise, citrine, emerald, garnet
Cool
You have pink or blue tones in your skin, and ashy, cool brown to black, or platinum hair naturally. Your veins appear bluish.
Best Metals: White gold, platinum, silver, tungsten
Best Gems: Ruby, Tanzanite, pink or blue sapphire, amethyst
Neutral
You have both warm and cool coloring, your veins have a mix of green and blue, and a wide range of colors suit your skin.
Best Metals: Lower purity gold (10k), white gold, platinum, steel
Best Gems: Diamond, opal, pearl, any color sapphire (they come in every color!)
Olive
You have fair to deep skin with a greenish undertone. You likely tan easily.
Best Metals: Yellow gold, white gold, rose gold, platinum
Best Gems: Padparadscha, sunstone, brown diamond, turquoise