I always have earrings on (two pairs), regardless of what other jewelry, or lack thereof, I'm wearing. The top pair is usually diamond studs, but I'll swap them out for other things too. If I'm wearing a statement necklace, then I'll usually wear simple hoops, studs, or pearls. Occasionally I'll do more prominent earrings with a statement necklace, or wear two sets of larger flashier studded back earrings. I have no qualms mixing gold and silver (and copper and rose gold and bronze, for that matter), especially if looking at just the setting of small earrings. Many of my statement necklaces are gold, and my little diamond studs have a silver setting so I've got auto mix right there. I really think you'd be just fine wearing silver set earrings with a gold necklace. I wouldn't match the stones though, wear something that's similar but not the same if you feel like wearing something that matches more.