There isn’t any one right answer to this, because it’s connected to an economy very different from anything we’re familiar with. There are at least three ways to approach the question; none is perfect, and they crank out different answers. And in addition, it’s not clear to me which coin a “piece of silver” would be. I’m guessing a denarius; because that was the standard Imperial coinage, and coining precious metals was an Imperial monopoly. But the drachma did circulate, and Tyrian shekels were used in Jerusalem as Temple coinage. Anyhow, let’s think in terms of denarii; that’ll get us within an order of magnitude, which is as close to accurate as we can expect to get anyway.
WEIGHT OF SILVER. This is used most often, but I think it’s the least useful. First off, it depends on the modern silver market, which fluctuates. (So, modern market fluctuations affect first century currency values…?) Second, silver coinage in the Roman Empire was rarely pure silver, and the amount of actual precious metal in a coin of a given weight could vary dramatically.
EARNING POWER. This is helpful, I think; but remember that we’re dealing with a third world pre-industrial society in which there was very little like a “middle class.” Most people were poorer than we can easily imagine; a few were spectacularly rich.
So, it looks like in Judea a day laborer might earn a denarius a day; if he could get work. It also looks like most people hoped to work seven days a week; although observant Jews, keeping the Sabbath, would be an exception.
An artisan might expect to earn two denarii a day. So one to two denarii a day look to me like the normal range.
So: in terms of earning power, thirty pieces of silver would represent something like two weeks to a month or more of wages. Bear in mind that a household probably had more than one person working full-time.
COST OF LIVING. But what would you buy with it?
Here things get tricky. The cost of food varied considerably; it might be relatively affordable in a rural area if the crops were good, and much higher in a city or if there’d been a local crop failure. (Transportation was generally poor, so you couldn’t much compensate by shipping in food from outside, unless you were right by a seaport.) The cost of manufactured goods like cloth was much higher, comparatively, than we would expect; everything was hand-made. An ordinary person would think in terms of one outfit of clothing a year, and you’d wear it till it wore out.
As best I can tell, a denarius a day would probably be enough (though barely enough) to maintain a small family at subsistence level. “Subsistence level” being lower than urban poverty in any modern industrialized society.
So, you could maybe meet expenses for a month with thirty pieces of silver. But then, you can get an argument among scholars whether Judea was a cash economy in the first place; or were most transactions done by barter?
SUMMING UP: I don’t see any reasonable way to set a “dollar value” on thirty pieces of silver. There’s too many different plausible questions.
The best I could say was that thirty pieces of silver would be a sizeable amount, for an ordinary working person; but far from enough to set you up for life. I’d guess that if you think in terms of a month’s wages, you’ll have some sense for how such an amount would feel to a person in that society.