I've gone for something a bit different, not to say the there's anything wrong with the previous builds, this is just another way.
My basket at Overclockers UK:
Total: £392.15
(includes shipping: £12.30)
I've stuck with in stock items, so the Microsoft Keyboard is out, but I would have selected it if it had been available.
I've gone for the cheap mobo/i5 build rather than the mid range mobo/i3 builds. With the i5 I don't think you need to upgrade for some time and when you do, just go the whole hog and replace the mobo as well. Most people never get around to upgrade their CPUs, and starting from an i5 you'll less like to need to. NB: OC forum members are not most people.
Does he need a better mobo? Probably not. If you not overclocking, adding lot of extras/Peripherals (13 year old will have limited spending I guess) I don't see the point.
You'll notice a few omissions, No SSD, Graphics card, Wi Fi? how is it being connected to the internet?.
There is £107 remaining in the budget.
I would say consider looking at the 2nd hand market for the GPU, you should be able to get a GTX670 in the £60-£90 range. (Just sold one of mine for £85)
The AMD equivalent cards cost a bit more on the 2nd hand market as coin mining is still boosting the prices.
And the rest for a Wi-Fi Card/dongle if required, or headset, or small SSD for OS, or DVD-RW. If you need more cash for these extras you could down grade the CPU to the i5 6400 for £20 less.
So if your prepared to go with a 2nd hand GPU you get a significantly faster machine from the start.