I have gone for the basic Yamaha one from the shop you linked to at £619 plus £60 odd for the stool. It's more than we wanted to spend really but it has a lot of the features you mention and hopefully it will last a long time.
It has a stand built in and I think I will look for somewhere local to buy headphones so DS can try them on before we buy.
As a primary school TA I have taught 'informal' music lessons on recorder, percussion and keyboards. By 'informal' I mean it was for fun only, with no aim of taking Grades.
First things to consider are: must have full-size keys (even though he is small now, he will grow, and mini-keys are very restricting.)
Have as many keys as possible, at least 61 (or you will run out of notes for piano music.) I see Yamaha do a new Piaggero series with 76 keys.
Have 'touch sensitivity' like a 'real' piano, so you can play with more expression.
Although keyboards and digital pianos LOOK very similar, the technique of playing is totally different between the two. If you are expecting him to play Classical music in a serious way, (difficult to guess at age 5, though of course Lang Lang was well on his way by then!) then a Piano would be better. However, if you only expect him to play for fun, but maybe take some Grades eventually then a Keyboard is probably better.
In case you are not aware of the differences of Piano vs Keyboard techniques, to play a Piano (digital or 'real) the left hand has to play an accompaniment to the right hand melody. On a Keyboard, the melody is still in the right hand, but the 'accompaniment' can be automated, needing possibly only one note from the left hand. Keyboards can also 'sustain' notes, that is hold them on for a longer time, whereas Piano notes fade away quite quickly.
[If you already know all this, I apologize for going into all this detail.]
Digital pianos and Keyboards can be connected to amplifier systems and speakers, for a larger sound, and stereo spread between the speakers. Both can also be connected to recording systems and computers for recording and multi-tracking, building up compositions layer by layer.
A digital Piano will have several, mainly 'piano' type sounds, such a grand piano, honky-tonk, harpsichord, vibraphone, etc. A Keyboard, on the other hand, will have several hundred sounds - orchestral, brass, woodwind, many types of organ, many types of guitar and bass, plus, usually 'keyboard percussion' with each key having a different percussion sound on it, drums, tom toms, cymbals, hi-hat, wood-blocks, and assorted Latin percussion sounds. Thus you can play a simulated 'drum solo' 'live', or program it into the recorder. (I was a drummer for 40 years, in big bands, country rock, pantomimes and stage shows etc, hence I like the drum features!)
One thing I would steer clear of are features that claim to teach you to play by following coloured lights above the keys; it is much better to learn properly to read music without any gimmicks. And it is NOT as difficult as you might think.
You will also need a good strong stand, unless you go for a Piano that has its own body. Also headphones, for private practice, and cables if you are wanting to connect to other equipment.
I came across this dealership, but there are, of course, many others equally good: