Once you've figured out what size bike you should be looking for, you'll need to know the difference between different types of construction. You have a choice between steel, aluminum, carbon fiber, and titanium. I don't know anything about titanium, so I can't speak about its good points and bad points, except to say that it's very light. Aluminum is also very light, as is carbon fiber. The downsides of aluminum are that it gives a harsher ride than steel, and that it develops stress fractures that eventually will break the frame. Buying a used aluminum bike is a huge gamble, because you don't know how hard it's been ridden, and thus, you don't know how close to structural failure the frame is. The same structural failure problem applies to carbon fiber.
Then there's steel. It lasts and lasts and lasts, and the better grades of stel are as light as the aluminum and carbon fiber bikes. A steel frame will not develop stress fractures the way carbon and aluminum frames will, so you can use it year after year after year without worry.
There are different grades of steel, ranging from heavy high tensile (hi-ten, known derisively as "gaspipe"), to high carbon steel, to the top grades of butted Chrome-molybdenum or Manganese-Molybdenum alloys. These last two are the most desirable grades of steel bikes. Butted tubing means that the tubing thickness varies, with a thinner gauge in the middle to cut the weight, and heavier gauges at the ends, where the stress points are. Butted tubing can be single-butted, double-butted, triple-butted, or quad-butted. Single-butted is thicker at one end, and thinner at the other end. Double-butted is thicker at the ends, and thinner in the center. Triple-butted is thinner in the center, and has two different thickness at the ends. Quad-butted has two different thicknesses in the center, and two different thicknesses at the ends.
You also need to look at the construction: was the frame lugged and brazed, or was it welded? A lugged frame is one that has the frame tubes inserted into lugs, or sleeves, and brazed. A welded frame has the tubes welded directly to each other. Some wleded frames are high quality, some are very low quality. High-quality welded frames should have smooth angles where the tubes meet; low-quality welded frames will have sharp angles where the tubes meet. Somebody else here will need to fill you in on the merits of different types of welded frames.
Generally speaking, a high-quality vintage bike will have a butted Chromoly lugged steel frame.
Then ther's the question of which manufacturer. I haven't ridden a Japanese bike, but from what I've read here, they made very high quality bikes, and i would seriously consider looking at
Japanese bikes. I have ridden French-- I have a Motobecane, and love it.
However, there are a few idiosyncrasies that you need to be aware of. French bikes willl have either French thread or Swiss thread bottom brackets, which many bike shops don't know how to service. They can be serviced, just be aware that some bike shops are more competent than other bike shops. The other service issue with vintage bikes that bike shops raise is that they have freewheels, rather than freehubs. That's not a real problem either, but some bike shops will make it seem like it's an issue.