Even experienced operators of wood stoves can easily miss damage that would make the stove unusable, so there's always some risk involved. If you're new to wood stoves, I'd seriously consider buying new.
That said, you want to look for warped metal, discolored metal, anything which would be a sign the thing was severely over-fired. If you find a crack or an opened weld seam, that's obviously a no-go situation. Make sure door is plumb and square, and closes evenly, and if there's a bypass damper, make sure that operates properly and isn't warped (common).
Knowing the stove model(s) you're looking at can give more targeted advice, as different models have different known weaknesses / fail points.
You'll probably also get endless advice about checking gaskets, "dollar bill" tests, and other BS. None of that matters, as gaskets and door adjustments are regular wear-and-tear maintenance. Don't judge a used car by the condition of its windshield wiper blades.