I had been thinking of something similar for my lads, they both share an old Q9550 full ATX system which I think probably draws a bit too much power considering their abuse of it and the games they play, homework etc.
Not made my mind up on that yet, I have a 350w and 450w PSU and couple of Micro-ATX cases, so would only need a CPU/Mobo/Mem/GPU.
They have a 500gb Samsung HDD, and to be honest don't seem to need more, they even ran with a 120gb Samsung Evo for a bit but that ended up in a media pc I was experimenting with. For now it is just the single 500gb HDD they use. To be honest I doubt they would ever need more than 120gb for the OS drive and 1tb of storage and that is a three account PC.
Some items I would have been considering for a kids Mini-ITX build, the hardest thing is choosing a case that, A; is within budget, B; Allows decent cooler choices, C; The kids think looks cool!
YOUR BASKET
1 x
EVGA GeForce GTX 750 SuperClock 1024MB GDDR5 PCI-Express Graphics Card (01G-P4-2753-KR) £89.99
1 x
Asus H81I-Plus Intel H81 (Socket 1150) DDR3 Mini ITX Motherboard £58.99
1 x
Intel Pentium K Anniversary G3258 Socket LGA1150 Processor - Retail £57.59
1 x
OCZ Arc 100 Series 120GB 2.5" SATA 6Gb/s Sold State Drive (ARC100-25SAT3-120G) £56.99
1 x
Zalman M1 Mini-Tower - Black £55.99
1 x
Avexir Core Blue Series 8GB (2x4GB) DDR3 PC3-12800C11 1600MHz Dual Channel Memory Kit (AVD3U16001104G-2CW) - Blue Light £49.99
1 x
Seagate Barracuda 1TB 7200RPM SATA 6Gb/s 64MB Cache - OEM (ST1000DM003) HDD £44.99
1 x
Antec VP350P 350W '80 Plus' Continuous Power Supply £31.99
1 x
Silverstone Argon SST-AR01 CPU Cooler - 120mm £25.99
Total : £486.61 (includes shipping : £11.75).
Of course it takes you over the budget, but it only provides you with alternative items to look at, my lads play a few games and I think a 750 GPU would be the minimum, otherwise they are as well with just a console.
My opinion was that the Intel performs well and as the Mini Nvidia 750 GPU needs no power cable, yet plays most games on a 1080 monitor, it would save in electricity, heat and noise.