There really is no definitive answer to that question, but one should always remember that you will be listening to, and looking at your piano for a long time. The average lifetime of a piano is around 60-70 years, and you will probably have it for a lot longer than any car, or even house! Pianos generally depreciate very little, and a used piano that was built 20 or 30 years ago, providing it has been well maintained, will cost almost as much as a similar new piano. So, always buy the best piano that you can afford. And when considering a child who is starting lessons, a good quality instrument is vital in keeping their interest healthy in learning to play.
Size of the instrument is also an important thing to consider. If you have the space for it, always choose a larger piano over a smaller one. The longer strings and larger soundboard will result in a superior tone quality than you would get in a smaller piano, and you will also benefit from a stronger and clearer sound from a larger piano.
As for makes of piano, we have listed a few of the more famous makers' names on our main site, which you can access via this Famous makers link, but we would love to hear about your piano, and whether you would recommend it as a make? If you had to change your piano, would you go for the same make again, or would you maybe try looking for something different?
Personally, i am very fond of my own Bechstein upright, which has a lovely mellow tone, and a beautiful, smooth feel to the action. If i had to swap it, there are many makes of piano out there that i would be more than happy to own..... But, i do love my Bechstein!