Mini ITX Build £450-500

and ATX

Oh really? That's pretty good, those boards must not come that far over these waters to new zealand :p

It was a £10 difference. I guess the locked one would work too, no need to overclock anyway. I was more thinking of future expansion with that one. An unlocked cpu would allow it to be pushed to extend its life a little longer if they upgrade the gpu.

Yes, contrary to popular belief, you do not need 8GB. It may come in handy for the activities she wants, but when using shadowplay, it's kinda useless. In this case the GTX770 will do what she wants quite easily. The majority of games never exceed 3GB. They build a good amount of Windows games with 32bit windows 7 in mind. As you can only use a max of 3GB in that OS. Until you get to 1440p and beyond, 3GB will work. The only exceptions are heavily modded games. It reminds me of those people who push SSD, yeah SSD's will make loading times faster but at exponential costs. Along with known write issues on SSD, I could never wrap my head around that concept of SSD necessity, an HDD gives more space and has had extensive more time being tested... It's still the better choice over SSD.

Yes,

Micro atx and amd is a big no-no.

For smaller systems just use intel , this is not only for the board support , but also for the heat management.