If I were you, I would care only about the sustain, and made sure the piano and the pedal support more than just on and off states.
Surely, if your son keeps practicing there will be a time when the other pedals will start to make a difference. However, you should think then about getting an acoustic piano.
The three main pedals of the piano are:
- the first (right) is the sustain pedal,
- the second (left) is the soft¹ pedal,
- the third (middle) is the sostenuto² pedal (it might be absent in some old pianos).
The first one is essential, moreover, you want the piano to recognize more than just on/off positions, that is, the so called half-damper or half-pedaling. Even early pieces may use this feature to great effect and you would like your kid to learn that the pedal is also to be played, not just stepped on.
The second pedal changes the timbre and using it is actually an advanced technique. There are several points to make:
- I don't know the percentage, but many people won't hear the difference (some are unable to hear, some don't pay enough attention, some dismiss it as something else, whatever).
- Notation for the second pedal is quite rare, most often it is a subject of interpretation. Knowing when and by how much is not easy, but at first that can be supplied by the teacher.
- When pressed too much, most low- and some medium-quality acoustic instruments sound like a cardboard box. Personally, when unsure, I prefer to avoid it (on such instruments pressing very little doesn't make a difference) rather than ruin the sound. BTW, this is a nice cheat if you would like to assess the piano quality fast.
- Keeping the pedal at precise position one wants for a longer time when playing can be hard.
Summing that up, the second pedal won't matter until later, and when it does, then a lot of other details will matter too, so it's better to consider an acoustic instrument.
The third pedal is mostly used for more advanced pieces. Please note that although it has a reputation for being an advanced technique, there is nothing complicated with it, really. On the other hand, it actually becomes useful only when two hands is not enough, e.g. with complex chords, too big spread or convoluted poliphony. For example, the first time I've used it was in some Rachmaninoff, while the first time it made a big difference was d-minor fugue from Shostakovich's Op. 87 (that piece is hard to forget). In other words, even if its usage is rather simple, it is not useful to a beginner musician (one case where it is useful: practicing jazz scales or progressions, where your left hand uses voicings that sound terrible without the bass note, but you can use also some play-alongs for a better effect).
I hope this helps ;-)
¹ The soft pedal of a grand piano shifts the hammers, which makes the timbre different. On upright pianos it only brings the hammers closer, so the sound is softer, but the timbre stays the same.
² The upright pianos rarely have the sostenuto pedal, instead it's usually the "practice" pedal which slips a layer of cloth between the hammers and the strings, so the piano is much more quiet.