If your child is following the Wunderkeys programme, a basic keyboard is fine. If they continue to enjoy lessons and want to carry on more seriously then I would recommend buying a piano.
I remember my first piano I played on as a child. It was given to us by my grandparents and was more of an antique than an instrument. It had beautiful walnut panels, inlaid marquetry, candlestick holders and I’m sorry to say, ivory keys. It sounded like a honky-tonk piano and needed frequent re-tuning as the frame was made from wood (modern frames are metal). My piano teacher told my parents that I needed a better instrument if I wanted to continue seriously with the piano so they found me a more modern piano.
I would definitely recommend steering clear of any pianos which look pretty but are more antiques than instruments like my first piano. Don’t be tempted to buy something on ebay without trying it just because it is very cheap. You’ll only end up putting it on the bonfire!
The top piano names are: BOSENDORFER,FAZIOLI,STUART AND SONS, BECHSTEIN,MASON AND HAMLIN CHARLES R. WALTER, KAWAI, YAMAHA, BALDWIN,STEINWAY & SONS.
If you can afford a Steinway, this is the piano of choice. However, Steinways are generally not affordable for most people. They do however have a slightly more affordable range of pianos called the Boston. The Boston pianos are designed by Steinway but are actually manufactured by Kawai. I personally own a Kawai as I like the tone and Kawai, like Yamaha is used by many music schools and conservatories in their practice rooms. Both Japanese makes are trust worthy. The Yamaha has a brighter tone than the Kawai and tends to be a little more expensive but I think you are paying more for the name. They are both good pianos but you get more for your money with a Kawai.
If you need an instrument that you can play without disturbing the neighbours then you can get pianos with a practice pedal. This is pedal on upright pianos that is depressed and moved across that muffles the sound so you can play without making too much noise. It does however have its drawbacks as you cannot practise with the full range of dynamics. In this regard, a good quality digital piano is better as you can plug the headphones in and practise as normal.
Pianos are a bit like cars. Once they are taken out of the showroom, they depreciate quite a bit so I wouldn’t recommend buying a brand new piano. There are some large specialist piano auctions where you can pick up some secondhand bargains. Just make sure you test them before you bid!