Beware of records pressed on lightweight polystyrene rather than vinyl. This is an exclusively US thing, very common on 45s but also found on the LPs of certain labels, especially US Decca/Coral/Brunswick from the 50s, early Pickwick and Halo/Rondolette budget albums, and some smaller New York based labels of the 50s and 60s. The styrene LPs stopped coming around 1966, but the 45s continued well into the 90s.
Styrene pressings "ding" instead of "thud" when you tap on them. They're very lightweight but usually pretty thick. The labels are often (though not always) glued onto the record surface rather than pressed into it, or else printed directly onto the plastic.
The reason you should care is that groove damage is invariably much worse with styrene--it's a softer surface that can be chewed to bits by a worn or misadjusted stylus, or one that just contacts the groove wall in "the wrong way". I've heard some very expensive brand-new cartridges that, for whatever reason, eat styrenes for lunch. I have a box of never-played styrene promo 45s that I keep for testing new stylii for my V15-VXMR. And some of them flunk!
I'd say about 60% of the styrenes I've purchased have had problems, even if they looked stone mint. It's a good thing to watch out for to avoid disappointments and properly assess the gamble you're taking. Look for whitish-looking groove damage, even very slight--that's usually the red flag on a styrene pressing.
All used records are a gamble. Just accept it, make your best guess, then chance it. And you're allowed to buy fried records if you still think you'll get enjoyment out of them.