What should I look for when buying a piano?

The easiest way to buy a piano is to go to a reputable music store and try out all their pianos.  If you don't play, take along a friend who does.  If you can't find anyone to go with you, ask the salesperson to play any and all of the pianos that might be of interest to you.  If they won't do that, go to another store.

Music stores are almost always more expensive than private sales -- they have to be, to pay their staff and the electric bill.  But when you buy a piano privately, you don't get a warranty and can't take it back, so you have to know you're getting something good.

The best way to do that is to take your piano technician with you to check out the piano.  I gladly do that for my customers, because I want them to get the best piano they can afford.

If your tech can't or won't go with you, find out who has been working on the piano for its current owners, and talk to that person.  The owners don't remember who tuned it last?  They haven't had it tuned "for a while"?  Ah, well now you know something very important about the piano you're thinking about buying:  it has not been maintained properly.

That might not be the kiss of death, although it should make you much more cautious.  Some pianos are so well-made that they can survive abuse and neglect.  Others can't.  So now you need to know how to tell the difference.