Best type of metal for turntable platform?

I always thought copper would be cool. Trying to find a billet that big may be a problem...

I'd try a damping material between two layers of aluminum.

There are so many divergent theories on what an ideal platform for a turtable should do, and how it should be made. I've noticed lately that for high mass and unsuspended tables stainless steel has been popular. What turntable(s) are you going to use on this stand?

If you view this document -  Documentation of damping capacity of metallic, ceramic and metal-matrix composite materials (utexas.edu), it gives an excellent summary of the damping characteristics for metals.  Table III is the one of most interest, and the larger n^ (column to left of Remarks) the greater the damping. 

Aluminum by itself is not that great, so unless you revert to just mass (weight) as @slaw says two layer of AL w/damping can improve the damping considerably.  Also, viscoelastic damping can be any thin film plastic that can stretch at room temp.  Ideally, the two plates are different different thickness (and different stiffness) so that the thinner plate is the constraining layer that along with the viscoelastic damping are what damps the thicker plate.   The viscoelastic damping layer can be as thin as 0.015" and be very effective.  If you then add another layer - its damps even more, but the first layer get you about 85%.

Modellers Clay such as the Brand Newplast  has exceptional damping properties and will be quite valuable as a material when used with 
materials that have structural and mechanical properties.