Woofage is right about underdamper.
Also, cross-strung (where the longest strings cross over the shorter ones, in different planes) will give you a better tone.
Arcoleo: I have never heard of a piano whose sound board was made of anything other than wood. Frames should be iron.
Another perfectly acceptable make not mentioned is Rud. Ibach Sohn. I had one of these, given to me by a friend's mother, when I was in my teens. I got up to about Grade 7 on it, but being an overdamper model it wasn't as good as the pianos at school so I generally practised on them as well. Overdamper pianos are generally less responsive and you won't be able to play very fast pieces on them, especially if there are rapidly repeated notes, because the mechanism takes too long to return to its resting position.
Bechstein are wonderful and you won't find a cheap one. You can look up the frame number on the Bechstein website and find out your piano's age. ICBA to look inside my piano atm 'cos it's covered in crap, but IIRC it's from 1891. I think you might be able to do this with other brands as well.