I think for a young student it does not make sense to buy a piano, and certainly do not buy a new one. (Actually, I would never buy a new piano under any circumstances. I would buy a quality used piano from a piano tech instead.)
For now, you should find a small, portable electronic piano with built-in speakers and full-size weighted keys. Specifically, I suggest you look at something in the Casio CDP line. Casio has really stepped up their game in the last ~ 10 years, and these keyboards are a remarkable value. They action and sound of these pianos is pretty decent, plus there’s a headphone jack for silent practice. If only violins had that too. :p
New they run $300 – $500 depending on the model, but you could even find a used one for less. You’ll also need a stand and a stool, and you’ll also want to get a proper sustain pedal instead of the sewing machine pedal that it comes with. Yamaha makes a nice one that works great.
After a few years, if your child’s interest in the instrument is still going strong, you can think about upgrading to a better instrument and sell the Casio.
