Shielding a PC is not done to make it work better (unless there is a radio/TV transmitter nearby that needs to be excluded from the PC's circuits); it's to prevent the PC from interfering with other equipment. If you live in an isolated farmhouse and find it doesn't bother your use of other devices, then none is needed*. If you live near other people, the latter may come looking for you if they are on the receiving end of your interference. (A portable radio with a ferrite antenna on the AM band makes a nice direction finder.)
A slip-in peripheral may indeed create a hole in the shielding. A PC gets tested for RFI approval by running it in all of its saleable configurations (with or without a CD drive, for example), and then on top of that, has the cables moved around to find the worst possible position. Then if it passes, it passes; if not, back to the drawing board. An empty PC case, on the other hand, has nothing to test, so I don't think there is a way to "approve" them. They probably just get designed as if they were going into a system that would require approval (if you're lucky).
I see nothing wrong with aluminum foil. Oxide is of course going to coat the surface, but so what? If that is not conductive, then the RF will pass through it and "find" the aluminum below. Else all the aluminum equipment cases in the world wouldn't work either, because they would get "all oxidey" too. Oxide does present one problem, and that is preventing the intimate joining of different pieces of foil if you can't do the shielding with one large piece. Poor connections is the reason we gave up on aluminum house wiring. You could fold the edges over several times to increase thickness and then fasten those together with small machine screws and nuts or with backing washers, Pop rivet them together. Or even inexpensive small eylets could be used as rivets. Copper or brass would be better on this aspect because it could be easily soldered at the seams. Copper shielding tape (conductive adhesive?) can also be used for joining or as shielding by itself for difficult areas (like a the inside of a CD-player front plate).
The increased conductivity of copper theoretically makes it a more effective shielding material, but I don't know if you could even detect the difference, either by measuring or testing with target devices. You might need to be shielding a high-power transmitter to tell the difference. Everyone has seen zillions of those little tinned-steel shielding boxes in TV sets, game consoles, etc. and we all know how crappy steel is vs. copper, yet they are designed in. I think it just makes us feel good to know that there is copper in there when, practically speaking, an old tomato soup can might be close enough to perfection.
That CRC shielding spray Baliszoft suggested looks a lot easier to use on a wooden case instead of lining it with metal. You would need to figure out how to connect to it to bond all the shielded parts together. And I'll bet it is expensive, just because they can. (No pun intended, but enjoy it anyway.)
For holes nullifying the shielding, it depends upon the frequencies you are trying to block. If you want to really get serious use inch-thick copper honeycomb, or the equivalent made by joining lots of tubes together to simulate honeycomb. Nothing says "cool" like a shiny big exhaust stack sticking out, especially if you do a nice neat soldering job.
You can buy ferrite cores that snap shut over external cables (like handcuffs) to block RF from using them as antennas. (I always save them if I am junking something that has them.) I think RS sells them. If you dismiss them, then go to bed thinking about the fact that your power cable is UNSHIELDED! And that it plugs into a receptacle fed by UNSHIELDED house wiring. That's it, your whole house has become the enemy. Sleep tight.
Bond all shielding together in as many places as possible.
Whatever you do, get that battery-powered transistor radio out, tune to a quiet spot, run some software and test before and after your efforts, keeping all other conditions the same. If you didn't do any good, tell us and we will all write you notes of commiseration and say, "There, there, now."
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*Exception: Keeping radiation in is important if you don't want spies reading your data, say if you're moonlighting for the CIA or something like that.