Let's start the componentry discussion. I'm sure both of you dudes/dudettes following the project want to know about the intricate variations in every possible way of how this thing can go together, and in positively excruciatingly fine detail at that.
...yeah, right. [insert "rolleyes" smiley here]
More seriously, though, it's worth expounding on the parts at least a /little/. There are design considerations here. For now, let's look at the chassis, since that's the most important and basic part, at least in a sense -- everything attaches to the chassis.
The object I chose for the chassis was inspired by a photoset I found on Google Images, posted to Imgur here --> https://imgur.com/gallery/mOyf8
(Full Disclosure: as I am a member of the Imgur community, I posted a comment to that album -- mine is the comment about cooling.)
Strangely, until then, the idea of placing the guts of a computer in or on a three-ring binder somehow had not occurred to me. This is very strange, since it's almost perfect for what I want to achieve here. The hinge is already in place and (as long as one doesn't spring for the ultra-cheap ones made of thin awful bendy plastic sheets) the rest is fairly sturdy. The only thing is that you need to toss the three-ring mechanism, which, as it turns out, is extremely easy. Give it a solid yank and it will come right out, rivets and all!
Suitable binders (the kind with thin PVC or whatever over cardboard) are also incredibly easy to find... Dollar Tree has them (I can't speak to Poundland in the UK, or equivalents in Europe, sorry), Wal-Mart has them, nearly everyone but the grocery store has them. A one-inch model will do fine in most cases.
The key, again, is that the sides have to be sturdy and rigid. If you get one with floppy, saggy sides -- congratulations, you just wasted 88¢ or so on a piece of $#!* that won't work here.
The other thing is that the hinges don't have a travel limit. This is easy to fix -- a simple folding flap of cardboard on the back of the binder props it up just fine. It's not like this thing is water-resistant anyhow...