This was a surprise present for a friend's birthday and it went down very well indeed!
I watched PCPartPicker and compared loads of hardware reviews in the months beforehand to get the very best performance for the price. The target was £300, but Windows tipped it over a fair bit since I wanted to be safe and avoid dodgy eBay resellers, having read about time limited keys and the like.
I was getting a little worried about the screen and left it quite late, but this very nice 19" Acer monitor showed up in a local charity shop for £10. While a widescreen HD screen would be nice, this will do for now as an entry into the world of PC gaming.
The PC went together really well, but I had trouble in that the DVI to VGA converter hit a bit of the case. Weirdly, the case overhangs the PCI-E backpanel by slightly too much for a DVI connector to fit. In the end, since we didn't have any HDMI to VGA converters and the screen was pretty old, I shaved the outer plastic coating off the converter where necessary and connected it up.
It has been running Skyrim and Space Engineers very well so far, though I have yet to test it on a larger screen pushing 1080p.