I have bought used bikes almost exclusively the past few years. The exception was when the frame that i am looking for is unlikely to be found or uncommon.

Here are some things i have learnt along the way:

Look for the frame that suit your purpose. Consider frame size, material (steel, alu, carbon), design (mtb, road, stepthrough, wheel size) etc. The frame i would say should be the, if not one of the most durable of parts, unless if it was used for stunts or extreme sports.

Bikes and parts are pretty robust, especially te metal parts. It is quite unlikely that you get parts near the end of their lifespan.

Dispensable parts would be the soft parts like grips, brake pads, tyres, saddles. These can be easily and cheaply changed and the condition of these parts does not affect my decision.

If you arenot familiar with parts, buy a big(ish) brand, which would more likely to have better parts. Buying complete with higher specs is cheaper and less work than buying low and upgrading.

Don't get these:
Plastic brake levers (makes braking weak)
Low end mechanical disc brakes (a big pain in the a** to mount, adjust, maintain)
7 speed freewheel or below (freewheel axle is supported far from the dropout, weaker design)
Friction/ratchet shifter (need more skill to shift)

Get these:
Full alu brake levers (eliminate flex from plastic)
Reputable disc brakes or any rims brakes (easier to work on, more so rims)
7/8/9/10 speed cassette wheel (cassette freehub is supported closer to the dropout, stronger design. 8/9/10 speed have more aftermarket options)
Indexed shifter (need less skill to shift)

The most important part to get right initially, other than the frame, is the rear wheel. Replacing a rear wheel is a bigger investment (cost plus shipping) than replacing other parts.