My lads PC, one is 10yrs old, the other is 12 yrs old and into his games. They have no complaints about ths system, it was a mix of my old gaming PC and another.
Asus Maximus II Gene LGA775 Micro-ATX motherboard.
Intel® Q9550 CPU
Corsair XMS2-8500 8GB (4x2) 1066MHz DDR2
BeQuiet Dark Rock Advanced CPU cooler 95 x 122 x 166
Sapphire HD4870 1gb Toxic GPU
Samsung 840 Evo 120gb SSD
Samsung F3 1tb HDD
BeQuiet PurePower modular 630w psu
Windows 7 Ultimate 64bit OS
Silverstone TJ08B-E case
My daughter's PC (6yrs old) Built with old HTPC spares and a few bargains.
Asus P5QL-VM EPU motherboard
Intel® Core™2 Duo Processor E8500
Corsair Dominator GT 1066c5 2x2gb memory
PowerColor SCS3 HD 5750 1GB PCI-E passive cooled graphics card
SanDisk Ultra II 240gb SSD
Windows 7 Ultimate 64bit OS
Corsair HX450w modular PSU
Samsung DVD/RW optic drive
Fractal Core 1000 Micro ATX case
Simple fact, no child NEEDS a £400 PC built for them, they do not NEED up to date GPU's if playing age related games or doing homework. They only need upgrades as they progress into usage of the PC that justifies the cost. My kids started like that, with me being into PC's tey will always get hand me downs though.
You started with a £150 budget and have a GPU, I have to say I am agreeing with the Quad core AMD budget offering. A budget PC case with a power supply included is £20 if you shop online.
Spending £90 on a case may be folly at this point, the system budget gains no benefit from such a case, a budget system will gain no benefit from a £15 or £150 case in a childs hands.
Spending £70 on a single 250gb SSD rather than £70 on a 120gb SSD and 1tb of storage? No matter what single SSD you get, if it's single it will fill up, no child will need 200gb of programs and OS space, they will need game storage.
£110 on a CPU when there most likely will be nothing your child is doing that an AMD 850K could not manage?
Of course all you need is a competent CPU, motherboard and 8gb or ram, with an adequate case and CPU, with your old GPU.
My basket at Overclockers UK:
Total: £273.03
(includes shipping: £11.10)
You could have course go even cheaper, there are Budget case/PSU bundles for £20. There are even cheaper AMD motherboard/cpu bundles, maybe even 4gb of ram.
That said, the following sort of items would be my choice if building my 12yr old a new PC from scratch and reusing an old GPU.
My basket at Overclockers UK:
Total: £746.78
(includes shipping: £0.00)