I'll actually be doing mixing/mastering more than recording. Tens of of fancy plugins, maybe even approaching 100 depending on the song, all running at the same time which is more intense than just recording, but still not too insane I think.
Dunno. I've been thinking about just going for Core i3. It should still be within my budget, and I want to get the best possible, even if something a little cheaper might be "good enough." Google results seem to indicate that it's generally better than some comparable stuff from AMD (correct me if I'm wrong), and the price difference from what I can tell so far is pretty negligible. RAM seems to be quite cheap so I'm not too worried about that. A 1TB Barracuda is like $80.
I'm not sure just what kind of power supply I'd need? I saw a Corsair CX430 for $17 after rebate?
I think the thing I understand the least is how to pick a good motherboard.
Do you know how to build a computer? If you do, then it should be straight forward and will get you better upgradeability for parts and a bit more performance. A pre made laptop also works. There are some decent $400 pc's out there right now.
Do you game or want to a tiny bit? Then AMD A8 or A10 depending on budget.
Just performance? i3 Ivy Bridge
For such a small budget and need, a $40 case with built in PSU would do fine. Or if you can get a free case from a friends old un used or broken dell, then yes, that $17 PSU (or just re using the one found in many computers) will be fine. You can get a free case or not spend money on a case and PSU if you ask around. Most old desktops use 300-450W PSU's with bad efficency but nothing that would affect a sub $400 computer.
At such a low price. It is a brain easy task to choose one. You should only use newegg or tiger direct or amazon of course. That already limits what you have. I recommend newegg, and then you look at what slots and ports you want on it. It should be around $50. Micro ATX at this price point gives better price to performance than a $50 ATX mobo.