When people talk about a bag, they talk about its size, its colour and its shape. The small metal parts get less attention, and they are the part your eye meets right next to your hand, your wrist and your jewellery. Zips, clasps, rings, studs and chain links are a bag's own jewellery, and they either agree with the metal you are wearing or argue with it.
Bag makers call all of these metal parts hardware. Three finishes cover almost every bag you will see. "Gold-tone" and "silver-tone" describe the colour you see, not what the metal is made of, so check the label if it matters to you.
Before you choose, look at the metal you already wear in plain sight: a watch, earrings, rings, a belt buckle, glasses frames, shoe buckles. That is the metal your bag will be compared with. You then have three options:
Pick a hardware finish and the metal you are wearing below, and read what the pairing does.
1. The bag's hardware
2. The metal you are wearing
Mixing gold and silver is common, and it works when it looks planned. Three habits make it look that way:
Count the metals you are wearing first, then decide whether the bag should repeat one, add the other, or stay quiet.
None of this is strict. A bag's colour can outweigh its hardware: a cream or tan bag usually looks right with gold, and a black or grey one with silver, whatever you wear on your wrists. A bag with a large metal logo plate is a different case, because then the hardware is branding and not an accent, and it will stand out whichever finish you pick. If you carry your bag across the body and your jewellery is mostly out of sight under layers, you can simply choose the finish you like best.
You can try all of this with a bag you already own. If you want a different finish, second-hand is a good place to look, and replacing a single strap or chain can change the metal on a bag you already like.