Veteran piano teacher here. You’re not unusual at all for starting your child at 4 years old! I’ve had many, many students around that age. Keep your expectations low and let the teacher teach… every tiny achievement gets celebrated at this stage and foundational work is being done even if it sounds like nothing changed from the previous week’s lesson.
As for what type of instrument to get… it’s up to you and your budget and space. For what it’s worth, however, the more “serious” the piano, the more “serious” the student and their entire family took things.
I had some who stuck with the little keyboard on a folding stand (without all the keys, but with all kinds of bells and whistles) and in my honest recollection not a single one of those went super far or even seemed to enjoy it all much.
Many went the “looks like a real piano but is digital” route, and I always felt that was the sweet spot. Older children could still play with earbuds or headphones or turn the volume down (please don’t let young ones do this; they need the feedback from those around them!) so if they REALLY got serious about it the family wasn’t being driven insane by constant practice. Younger children knew it was a real piano because it looked like one. And parents didn’t resent having the instrument in their space because frankly, they’re beautiful pieces of furniture and don’t look like an electronics store!
And then the majority just went with older pianos that were handed down or found on the side of the road or gifted for free or donated by a church. There is NOTHING wrong with those, but they do limit your ability to play or add stress if you’re in a multi-family structure! I’d also add that while a person your daughter’s age isn’t bothered by any “tinny” sound, please do prepare to invest in something newer in the future if she gets truly caught up and blossoms! Also, I’d suggest making sure whatever genuine piano you’d get doesn’t have chipped keys or dead keys; it’s very frustrating for small fingers.
I think my biggest concern is that somehow, those who said “we will start with a little half size keyboard and put it in their bedroom so if they don’t like it we haven’t wasted money” never seemed to fully support their child’s interest or be present when they practiced their little songs. (I’m not saying that would be you! It’s just a strange phenomenon I’ve observed over nearly 20 years.) Those who had a pretty piano in a central area seemed to take everything so much more seriously, and the smallest students seemed to be much more excited and comfortable coming up to a Real Piano - or something that looks like it’s real - and sitting on an Actual Piano Bench. The parents who expected their little ones to drag a dining room chair over or use a heavy chair nobody liked (that was inevitably the wrong height) just weren’t as helpful when it came to practice Ny, or bringing their child to lessons, or not canceling things. And little ones seemed to prefer a real bench/instrument over a shaky folding padded stool and a mildly tipsy little keyboard that always kept switching to the drumbeat setting.
I hope that helps, somehow. Again… do what you can afford! But do check out free pianos or digital pianos secondhand.
I’ve had incredibly talented absolute naturals who never went on to enjoy or stick with piano, because of lack of support from their families. I’ve had music students with learning challenges or who just weren’t naturals musically love every minute, play in all their spare time, and go on to literally attend college for music education… because of the incredible support and dedication from their parents.