Whether you're buying a new one or an old one, allow yourself plenty of time and try out plenty of pianos before making your decision. Take with you some contrasting pieces of music in order to try it out. Make sure you try high, middle and low registers, and try playing loud and soft, and something with varied dynamics, and something legato and something staccato - basically as many different things as possible to get to know the piano. It's good to be able to get a good dynamic range between very soft and very loud in each register. If you're buying a second hand piano, make sure you try out every note to make sure they all work and that they are all even, and make sure both pedals work. Good luck!
that's a simple rule, but remember that longer strings make better sound quality, especially in the low register. The laws of acoustic explain this. For a detailed discussion on this, you can read the "Reblitz" it is a book on piano tuning, repairing, even rebuiling.For a grand, this rule means the longer the better, and for an upright, of course "the higher the better".This is one important rule of course, but you have to take other things into account : quality of construction, age, etc.Another important thing : the vibrating flat piece of wood inside the piano that produces the sound ("table d'harmonie" in french, I can't remember your english word for that), is a vital and fragile part of any acoustic piano. If this piece has lost its internal "tension", or "load", the sound produced is weak / inexpressive. To keep that piece in a good state, especially over a certain number of years, it is of the utmost importance that the moisture rate of the room has been kept relatively stable in the 45% - 60% range and that large and quick temperature swings have been avoided. The problem is that you don't know that when you buy a second hand. But at least you can play the piano as much as you can and listen carefully to the quality of the sound to try to evaluate the actual state of the piano : if you don't like what you are hearing, don't expect too much from further fine tuning. Very weak high notes won't magically be cured by tuning or harmonization. Try another piano. The odds are that the piano is already giving the best sound as it can, so don't expect "miracles".Tip: if the seller tells you that the piano has not been played for years, and that it has been "rebuilt", this should not sound positive for you as a buyer. If this is true, then this means nobody has been paying attention to that poor piano for years and as a result, some structural damages have occured, and a major or partial rebuilding of the piano was deemed necessary. Therefore, I would advise you, as an unexperienced buyer, to favor a piano that has been played regularly, because that means someone probably took care of the piano.Ho, a last advise : it is not easy to sell a piano, so pick a fine one, because if you change your mind in 2 years time and want to buy a new one, it won't be easy to sell yours without a hefty discount...some piano sellers in Paris like to apply a 40% haircut on your piano (no joke!) so keep that in mind, flipping pianos is a very expensive hobby, so don't be shy and buy the best as you can, it will be cheaper on the long run than just buying a below average piano "because you are just a student".Thanks a lot for your advice, It was really helpful. So I will have to invest some time to start looking at pianos. Nice.