If you are going to take piano lessons, you do that because you like to play the piano or want to learn to play. Most of the time you play at home and that is also the moment when you enjoy playing the piano. That is why it is wise to choose an instrument that you can enjoy the most.
Regular (Acoustic) Piano
You need a regular piano to be able to make music properly. A regular piano has a precise touch with great dynamics (difference between hard and soft). The sound is full and can change the timbre due to the touch. You use the left pedal to play softly and the right pedal to make the tones sound. Often a piano has a center pedal. If you press and lock it, you can play very softly. It is a practice pedal, with which the people around you are less bothered by the noise.
A variant of the acoustic piano is the Silent Piano. That is an acoustic piano with a built-in digital piano module. You activate the hammers of the piano by activating the silent system. For example, the sound is muted and you can hear the sound of the digital piano through the headphones.
Alternatively, you can choose for a digital piano. The main advantages are that you can control the volume and even play with headphones. The disadvantages are that the dynamics (difference between hard and soft) are much smaller. Furthermore, the sound is always the same and the pedal does not last that long. On a digital piano it is difficult to develop a good toucher and a good expression. A digital piano is a good alternative for a novice student.
Below is an example of 3 different pianos each playing the same piano piece.
Simple digital piano: velocity sensitive but little expression (hard and soft), no weighted keys (little control over expression), simple sound (does not have a good piano sound)
Good digital piano: subtle dynamics, weighted keys (good control over expression), sound sampled from concert grand
Acoustic piano: subtle sound with rich timbre, refined hammer mechanism, sound generated by hammers striking strings
A grand piano is usually used for professional pianists. It has a richer sound than a piano and is much more dynamic. You can also play on a grand piano more precisely. Another advantage is that you can play softly with a different timbre with the left pedal. The grand piano mechanism makes it possible to play repetitive tones much faster and in a bound (legato) way. If a grand piano has a center pedal, this is a sostenuto pedal. With this pedal, you can love the keys you pressed and the dampers of the strings so that the tones continue to sound.
A grand piano is less pleasant for young children because the standard of the notes is very high.