How it sounds is the most obvious answer – but not the only one. Because a good violin that has been sitting for a while without being played will sound flat and the tone will be dull.
If you find a fiddle with good wood and carpentry, precision in the placing of the sound peg (inside) if the fingerboard looks good – find out if it has been played a lot and recently. If the answer is no, some sellers will be willing to let you return it after six months if the tone does not come alive – or you can takea chance and try bargaining down the price.
Obviously, the final factor is the sound – but how it sounds when you first play it may not tell the whole story.
And by the way – cheap violins can sometimes be very good, and expensive violins can be very bad. Price does not always tell the story either.
An excellent resource for your violin lessons need.