PSU: Any decent 80+ model, or one that comes real close (FI, even the non-80+ Seasonics). If possible, don't get a 500w+ PSU. If you need a 500w+ PSU, then have fun with the PC in the cupboard cooking, because I don't think it will work very well.
Fan: Nexus, Scythe, maybe Noctua.
As for the case, expect some Antec and Rosewill recommendations. You're going to find few cases, other than the P180, that will absorb much noise--you need to be creating less noise to begin with. Do not accept a case that does not have a 120mm intake and exhaust, and spend some time doing cable management.
In terms of upgrading, keep your power consumption down. I'm emphasizing this because you're both having problems with cooling because of enclosure for your enclosure, and wanting a high-power PSU (you may as well be asking for a giant SUV that gets 50MPG in the city). With a computer hutch thing, you have to choose one or the other, or put in plenty of time and $ dealing with it.
Less power -> easier to cool -> slower quieter fans -> less noise made -> less noise to worry about. To that end, don't upgrade to a video card that has a power plug, as one glaring example.
Another thing is to use beefy heatsinks wherever possible (FI, Ultra 120 or Ninja). If you can't exhaust enough air, you're screwed. But, if you just need more surface area or higher overall delta-T for the HS, then they'll do nicely.
On the off chance you're using a P4 3.06 HT, P4 E, or P4 D, Athlon Thunderbird, and/or a GeForce FX 5900, any upgrade to more modern components (A64 X2, Core 2 Duo; GF 7x00) will likely cause a significant net drop in power consumption, making things easier to cool, or offer better cooling options (socket T and the newer AMD sockets have much better HS options than say socket A or 423). Just something to keep in mind in case this is true, as you may want to hold off, and save up for a nice upgrade that may cure your problems.
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