I like your idea of having the PC in a different room than the actual screen and controls. But that's not really an option if you rent an apartment and cannot drill holes through the walls :)
Recommended cases: http://www.silentpcreview.com/Case_Basics_and_Recommendation...
They have similar recommendations for PSUs, heatsinks, fans, HDDs etc.
A friend of mine just picked up a Pentium 4 (yes all my friends have P4s), for £20, with a nice thick case, but the thing sounded like a helicopter taking off - the fans were so loud. We replaced the CPU fan (something like an Arctic freezer), and now it's quite easy on the ears.
My PC case is hugely bloated for my needs, I barely touch the DVD unit anymore, so I could just throw it in a trunk. Or make a new chassis for it. I only keep it as the size doesn't make me curse whenever I have to go in there. How about a piano stool for a case?
I think my favourite case I ever had was a micro ATX case that I modded to accommodate the PSU on the front. I could then keep it on the floor and still turn it off easily. As it was low down it was quieter. It also served as a rather nice foot warmer.
I had a friend with a Pentium 4 machine, that he just kept in a nearby cupboard. Once shut behind the door, you couldn't hear it at all. If I was a home owner (and could modify my house at will,) I'd probably just place my PC in another room (preferably a store), and channel cables through the wall. Would be cheaper than wasting money on over-priced cooling. The good thing about this, is that you also don't have to worry so much about what your PC looks like. You can even mount a motherboard in something like a biscuit tin.