The first and most important consideration when buying any instrument is the sound that it makes. As we have seen, when considering digital pianos, there's a strong link between the quality of the sound and the price you pay.
However, the minimum standard is still pretty high. If you're buying a first instrument for a young beginner, the sound of an inexpensive piano is likely to be perfectly acceptable, especially when taking into account that this year's budding Liszt may have discovered a completely different all-consuming interest next year...
The quality of the sound can vary in different parts of the keyboard. On cheaper pianos, you may find that the sound is fine in the middle register, but becomes muddy and distorted in the lower registers. The higher register can also deteriorate the further up the keyboard you go.
Both these phenomena are the result of cheaper sampling and sound reproduction technology - the electronic processes involved can change the essential character of the sound, even if the original recording was reasonably good.
The responsiveness of the keys is known as its touch-sensitivity, and is another mark of the quality of the piano. On a real piano, the sound becomes louder and brighter when you hit the keys harder, or softer and mellower when you play gently. The best digital pianos reproduce these characteristics with great accuracy, but you can also expect an acceptable degree of touch-sensitivity from lower-priced models.
Throughout this guide, the first consideration is always 'what do you need?'. If you're serious about playing the piano, then touch-sensitivity will be an important issue - your expressiveness will be shaped by the response from the keys and the speakers. But if you or one of your children are just starting out, then you can probably make do with a more basic digital sound.
One of the great benefits of a digital piano is that you usually get a choice of sounds. And not just acoustic pianos - you will often get electric pianos, organ sounds, and even strings. Again, consider your needs. A professional may want a small selection of excellent acoustic and electric piano sounds, while someone playing for fun may want more variety, with less concern for the realistic quality of each sound. Make sure the digital piano you choose offers the range of sounds that you need.
Some digital pianos have built-in effects, such as echo, reverberation, and chorus. Those with electronic organ sounds may also incorporate the sound of a rotating Leslie speaker. Take care when considering these options - the quality of the basic sound may have been compromised to allow for the inclusion of effects you don't need. If you're a pro, you will almost certainly have your own dedicated effects processor(s), which will generally do a much better job. But built-in effects can also enrich the sound and add an attractive dimension of colour and fun - it's for you to decide.