So you want to measure the first 15 harmonics of three phase voltage & power?
The minimum sample rate will be:
60(Hz) * 15(harmonics) * 2(Nyquist) * 3(phases) * 2(voltage¤t) = 10800 samples per second.
If you use a DSP PIC (say the dsPIC33FJ128GP302), it can run 4 sample/holds at the same time, or use the 12bit converter and DMA to automate the process. Either way it can run between 500KSps and 1.1MSps.
If you want much higher resolution, then you could use 3 cheap 24bit stereo ADC's running at perhaps 32KHz. That's a bit more complex to do, but I've linked a low end dsPIC with more channels than that at higher speed. But FFT's at this speed are not trivial on small dsp's.
Even if you have a single ADC & multiplex the front end - if you run it fast enough it won't make any difference to the end results.
I'd build the FFT and phase detectors first and see how fast I could get 6 of them running in parallel and what the RAM requirements are, then worry about the sampling regime.