You should use a mains transformer. Put a bridge rectifier on the output and ground the center tap of the transformer secondary. You will get +V on one bridge output and -V on the other. Put very large capacitors from each of these points to ground.
Then you can use the LM117 family of TO3 adjustable voltage regulators. The data sheets for these have examples of using external pass transistors for more current capacity.
I think flatulent has a good idea. You can add a source side fuse for short circuit protection and use a resistor + D/A + uC + LCD for a digital Voltage / Current readout or just incorporate some cheap meter movements into your box.