[dancing spawn of ungoliant]

One reason for using a ring could be that rings possessed at that time (I think) a certain value. They told the family the ring's bearer belonged, great lords had rings as a sign of their social status and they were beautiful things. Or that could be one explanation, why they made the nine, the seven and the three rings. Then Sauron made, as he was mocking all other ring bearers, a master ring.