Antique grinders are most likely going to be terrible as only in very recent years we have started making coffee that does not taste terrible.
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I don't think most antique grinders will grind well, you need ok burrs and somewhat tight tolerances. Do you have a photo of your machine?
I can tell you with certainty that grind uniformity is also very important and that's probably what you're gonna lack the most.
You can try using this tool by Unspecialty to get an idea of the grind size/uniformity without buying any fancy equipment. As far as whether your grinder is up to snuff, I think how the coffee tastes to you is the best determinant. If it tastes good to you, it's good coffee :)
How fine is fine? Fine for Turkish is basically dust. Fine for an espresso machine is smaller than table salt but not dust.
It depends on the brew method: finer for espresso, medium for drip or pour-over, and coarse for French press. Sometimes I grind my coffee a bit finer for a different taste.
Fineness aside, the main quality you want in your ground coffee is a very even size distribution around your desired size. If a lot of the resulting grinds are smaller or larger, especially very fine dust, the resulting brew will be much less balanced. If you want to, you can buy a sifter set to sort out different particle sizes. If you really want to, there’s software to do optical size distribution analysis.
There are specialized sifters to identify how many microns large the coffee is.