Best type of metal for turntable platform?

I would use a run-of the-mill Technics turntable as a plinth... completely immune to footfall.

What's the next problem?

BTW, there are plenty of round things that are designed to vibrate and resonate...look at bells, cymbals and drums. 

Going square is probably fine. Just decouple it and add mass (that doesn't have a very uniform grain structure). How about good old concrete?