Most often a chain first, then a bracelet, then a ring. A chain is the simplest to live with: it is worn inside or outside a collar, needs only a length decided, and asks nothing of the hands. It is the piece most people are already used to seeing on others.
A bracelet follows because it is more visible in daily life and shares the wrist with a watch, so it asks for a decision about weight and fit that is easier to make once the wearer knows how gold feels to wear.
A ring tends to come last because it is the most exposed to knocks, needs a size taken, and is the most deliberate statement of the three. The order is a common path rather than a rule, and plenty of people begin elsewhere.