Marble or Granite shelfs in a hifi rack?

It depends upon which frequencies you wish to isolate. Different materials have different characteristics. I know that marble cracks very easily, and that could be a problem. Granite "rings" if it is not real thick. Actually, a very dense wood like Cocobolo is better than either of those stone products.

Mapleshade likes thick maple, although I suspect it has a signature too. I'd just use whatever's easiest and most attractive for you, and then plop Neuance iso/absorb shelves on 'em for perfect isolation. Birch plywood's usually nicely made, and won't sag, unlike MDF. Don't make the mistake of believing that high mass is necessarily better. Marble certainly has a sonic signature, for example.
Make it light and attractive (NOT glass!), then float the Neuances, Rollerblocks or other high quality neutral devices. Have fun.

Twl-At what thickness does marble stop ringing?

Mknowles, I mentioned that Granite has that ringing. I didn't say that marble does. I think that marble, being a sedimentary rock, has more in common with limestone, than with granite. Therefore, I would guess that marble would not ring much, or at all. However, it does break very easily, if it is not supported fully from the bottom. As such, I would not expect it to be suitable for shelving on an audio rack.

As far as granite ringing, I know that 3/8" thick definitely does, and I haven't done specific tests on other thicknesses. I have read some material that referred to granite TT bases causing unwanted resonances.