I'm not sure about the meaning of:
it's good for your dime
Does he mean it is cheap?
I got moonshine
Drink it all the time
Goes down rough but it's good for your dime
You're correct, it implies that moonshine is inexpensive or cost-effective.
That last sentence, "Goes down rough but it's good for your dime" is saying that it may be difficult to drink but that is relative to the price you've paid for it. In contrast, a more refined liquor may be considered smooth (i.e., easier to drink) but it would be hard on your dime (i.e., costs more).
Nb. For non-North-American readers, a "dime" is a coin of currency in USA and Canada, and it's often used to refer to money in general.
In the "old days" (basically before World War II), a "dime" was a basic unit of American currency that was enough to buy a poor person's item like a loaf of bread, or a shot of (cheap) whiskey. A song popular in those depressed days was "Brother can you spare a dime?"
Because of inflation, that is no longer true; what used to be known as a "dime" store is now a "dollar" store or "99 cent store".
But the usage stuck in songs and poetry, and "good for your dime," means good for the "cheapest brand." Given its low cost, you can't reasonably expect better than "goes down rough" (but otherwise good).