*oh* that. For a single CORE setup, you can just leave the PIC ID to 0 since the first core has an ID of 0 (second of 1, third of 2, etc.). You can always update the ID later, though I can't remember if you can do that with MIOS via MIDI or have to program the PIC directly.
As far as the PSU, a small setup can get away with just using a linear-regulated wall-wart like
this. Depending on your SID model(s) and how you wire everything, you could go with a 9VDC linear regulated wall-wart too. Similarly, an AC wall-wart or power brick that supplies 9-14VAC should work (also depending on your SID model(s).
The reason you can do this is because the CORE and SID boards have their own power section which allow you to supply them with AC or DC. You do have to supply a little extra. You loose about .7 voltage from the bridge rectifier and typically the linear regulators need about 2VDC above what they regulate to work well. That's why a 12VDC power supply tends to work well, at least for 6582/8580 SIDs. For 6581 SIDs, you may need something a bit higher or will have to bypass the power section on that board and supply the chip with the regulated voltage from the wall-wart.
Point is, you can make it work easily with a single, simple, wall-wart and there are multiple ways to do it.
In a large setup, such as with a full control surface, 8 SIDs, etc. you will want something more robust most likely. The C64 PSU (or modern clones) can work well and there's some documentation on how to efficiently wire up individual SID modules with it. You can also buy multiple output high frequency switching or (expensive) linear PSUs. There's some really good information about these, as well as building your own PSU (not for the inexperienced or at least the careless!) on this forum in the Design Concepts and SID sections.
Since you're starting small, I wouldn't bother with those options for now, however. If you can get your hands on a C64 PSU, then you could use that. If not, I would just use a wall-wart.