you need to find someone who plays to take you to a music shop (and be prepared to hang around for hours while they try them out) you can always sell an unused guitar, so I would it's worth getting the best you can afford.
My DB got a guitar when is was a similar age, I am sure it was quite expensive at the time. It got played with a little and then set aside, as you'd expect . I may go for a cheapy starter one although they all seem to detune fairly quickly? What do you actually buy for more money?
'Traditionally' most people are encouraged to learn on an acoustic guitar and then move on to electric once they've mastered the basics. However, acoustic guitars are physically harder to play (the fretboard is wider and the 'action' i.e. distance between strings and fretboard is usually higher) so I'd recommend starting with electric. You'll be looking at around £100 to start with for something new and I'd recommend a 3/4 size guitar for a 9 year old. Something like this is a good bet: www.gear4music.com/Guitar-and-Bass/3-4-LA-Electric-Guitar-and-Miniamp-Black/7HD Since it comes with an amp, I'd recommend buying some headphones as well. I'd also recommend booking some lessons as well. You can find some good 'Idiot Guides' to guitar playing on Amazon, but it's always useful to have somebody show you the basic chords and some simple bits of technique.
We have a key board (and a piano ), so don't need any more of that kind of thing, I thought.
The e-guitar suggestion is interesting - he's never shown an interest and I am not sure I could cope .
I think I am going to go for one of the 'starter' guitars (some of them get quite good right ups by people who sound like they know what they are talking about or at least know the lingo). The main issue seems to be that they detune rather easily... We'll see. Should my brother be able to uncover his old guitar, we might be in possession of a rather nice instrument at some point numpty
DD2 has been learning guitar for nearly 5 years now. She started with a rented half size and then we bought a 3/4 size when she turned 8 (and she's relatively small so it was still massive on her). We got it from a specialist guitar shop and DD tried out 4 or 5 to see which she felt most comfy with. Apparently some of them have longer or shorter necks and resonate in different ways. The one we got was 100 euros including bag (about 85 quid?)
Now she's 11 her teacher has told us that in order to make further progress she needs a bigger guitar (7/8), but also one of better quality. Something to do with the quality of wood, I think, and the sound it produces. I suspect this new one is going to be closer to 200 euros, but at this point it's worth it because she's proved her commitment.
So to answer your question, I think the first one you linked to would come closest to DD's first guitar, suitable for beginner. Your DS would probably get 2 years out of it before needing a new one.