This is another topic that piano players and piano teachers will disagree on – which genre of music should you learn first? If you are only interested in playing one type of music, then the answer is really simple – you should learn first what you are interested in playing. If you are not interest in playing a genre, then there really is not much point in learning music that you have no interest in.
If you have some interest in playing music from all three genres, then I think the order you learn them in, does make a difference. Before I proceed though, I do want to point out that there will be some that will disagree with me, but also there will be others that do agree. I will try to endeavour to explain to you why I hold these opinions.
I believe that if you have any interest in playing classical music, then this is what you should learn first. Classical music, more than the other two genres will help you to learn to read music really, really well. With classical music, you learn individual notes before you learn to play chords, so you learn the structure of these chords and what notes make up what chords. I also think that because classical music has been around a lot longer than both jazz and modern music, by several hundred years, that both jazz and modern music have been significantly influenced by classical music and therefore both genres are a bit easier to learn with a classical music background.
Once you have learned some classical music, I would then recommend learning modern music. If you know classical piano, then learning modern piano is fairly simple and straightforward. Modern music uses a lot of chords, with most of them being quite simple, so learning the chords would actually take a reasonably short amount of time.
With the genre of jazz music I would recommend to learn it last of all because while it uses a lot of chords used in modern music, the chords tend to me far more complex and unusual. This is probably due to the fact that jazz music not only has European influences but African influences as well (this is not to say that African music is just one type of music, but rather many, many different types of music that all originated from the one continent).
On the whole, jazz music is harder and much more complex than modern music and that is why I would recommend learning it last.
I understand that many piano players usually stick to playing just one type of music, but if you happen to be someone that has a diverse taste in music and wants to be able to play music from any genre, then I hope that this gives you a better idea of where you should start.