Like Xigma said, wait til 2 weeks before the build. Also when Xmas comes around I am sure a lot of items will be on sale as they usually are around Holidays. Also the both of you could put it together. Have some bonding time or something.

It's still a good few months until Christmas. By then, prices will have changed and there will likely be sales on around that time so you'd be better asking for a build closer to the time of purchase. However, if the components were being purchased within the next week, this is what I'd suggest for around £350;
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