There are many wonderful piano teachers around, but along with those, there are also many who play piano themselves, but shouldn’t be teachers. That might be because they can’t express themselves well and explain the concepts, or it sometimes might be that they really don’t know much themselves.
Before you get a piano teacher for you or your child, make sure that music theory is included in the lessons — learning all about note values, timing, intervals, chords, and so on. It’s excellent if the teacher uses workbooks so you or your child can methodically work through theory step by step.
 

I’ve been asked that question a zillion times over the years and it always comes down to two factors, both of them personal: 1. Do you like the sound the piano makes (different brands have different sounds, obviously), and 2. Do you like the touch - how it feels to your fingers as you play.
That being said, I would also advise anyone to stay away from the off brands, of which there are many. My personal preferences are Steinway, Bosendorfer, Kawaii, and Yamaha, although there are certainly other good brands — but those are my personal favorites.
(We’re talking about acoustic pianos here — not digital pianos — that is a different subject we will take up another time.)