Assuming that a "piece of silver" was a denarius, how much would Judas's payment of 30 pieces of silver for his betrayal of Christ have been worth in terms of the average wage and cost of living at the time?

There were several monetary systems operating at that time and place. One might suppose that Judas was thinking of earning what the Torah called the "holy shekel", which meant that the money would have been pretty good. 30 shekels in that measurement was what the Torah said should buy off a slave, and might have also been used on a few months worth of food.

It is almost a certainty that the "30 pieces of silver" paid to Judas were shekels of Tyre, which were the only coins accepted by the priests of the Temple to pay the poll tax and for sacrifices. A shekel was worth about four denarii, so the sum would gave equaled 120 denarii. One denarius was the daily wage of an unskilled worker at this time, so 120 denarii would have represented about four months' pay. Most slaves sold for far more than this in Jesus' time, but it was still a significant sum. It's difficult to give a precise equivalent in today's money; some things were cheaper in ancient times (eg., food), and some more expensive (clothing). But around $5000 might be a fair estimate.