Frame, frame, frame. Lugged, double-butted steel always prefered. Cro-moly over Hi-ten. Reynolds 531 a sure bet. My size vastly prefered. Give any frame a good once over for cracks and dents.
After that, components. I've seen too many over dressed bikes-- what the heck are those Phil Wood hubs doing on that Murray?-- to ignore this. Find weird stuff-- a few nice leather seats, a vintage track hub, simplex retrofrictions, etc, etc, on the most unlikely bikes. You also see nice frames under-dressed at times, so component make isn't a sure sign of frame quality.
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