I'm as much of a DIY guy as anyone else, but building a quality computer power supply isn't exactly just a matter of throwing a few parts together. You need to first step the power down with a transformer, then use a rectifier combined with a capacitor and probably an inductor to smooth it out(BTW, if your transformer steps down to an RMS AC voltage of 12V, you will get ~17V DC out of it when you do all this).
As far as I know, most modern computer PSUs are high frequency switching PSUs, which has quite a few advantages in that the transformer can be much smaller and it's easier to get a smooth DC voltage out of it.
If you want to tinker with one of these, your best bet is probably to use an ATX PSU.