interconnects vs speaker cables vs power cords - which make the biggest difference?

My prescription has been IC, SC, and then PC.  YRMV. 

if you are tempted to spend more than $200 on all cables combined (for a normal sized home) then just hit yourself in the head with a hammer

Are you applying that to budget systems or any system?

My own experience and I believe the audio mags support power cord first then interconnect, then speaker cable.

As others have mentioned, it's system dependent.
With that said I'm going to answer your specific question and not get into other areas that you didn't ask about but others alluded to.
Power cords, interconnects and speaker cables in my opinion carry a signal or current of some type and can be used to tune your system (sound wise) to your liking. I find all three equally important.
If pressed to rank them in order, I'd agree with others that said:
1) Power cords
2) Interconnects
3) Speaker cables

Yep, Good quality Power Cables through some sort of Power conditioning 1st, then good quality interconnects 2nd. I just havn't been able to get big improvements with Speaker Cables so far, so a distant 3rd for me at this stage.