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?

@clearthinker

Rolls Royce solution: Take up the floor, dig out a bit if required, lay new DPC, in-fill with concrete screed, lower floor level to get more ceiling height if desired. According to taste, re-lay boards except where equipment and speakers are to stand. Or lay carpet.
OK there is a cost, but it will be worth it.

As I have stated, you can get the same results for much less, simply by reinforcing the floor joists in the area of the table. In fact, I would never do what you suggest without doing so first, because you are adding more weight to a poor situation. Again, this is not unusual in wood framed floor houses, both old and new. Renovations and remodeling is my business, and sometimes need to do this to clients homes, and not for audio reasons.

Let’s take an exaggeration; if your turntable is sitting on a trampoline, which you will also walk upon while using it, how much will you spend for a platform to remove the effect of the trampoline? That is allowing the ‘tail to wag the dog’. First, get rid of the trampoline, then see what you might need, if anything.

I did this in my house before getting the SOTA. I had a few 2x4’s left over from a recent renovation project, used about 3-4 to support the floor beneath by rack. Took maybe an hour. I could then walk, jump, etc. next to my rack which minimized floor fall issues to a great degree. I think we can make simple solutions and over-complicate them, and make them cost more than necessary.

@antinn , said it pretty well. You will not isolated the turntable from anything with whatever material you choose. You could actually make things worse. Sometimes a wall shelf will help, sometimes not. You have to isolate the turntable from everything about three Hz. Including the dump truck that just drove down the road. You can feel it even on a concrete  slab. The only sure fire way to do this is with a suspended turntable tune to less than 3 Hz preferably by hanging. SOTA and SME are the best at this. Sota's may look simple but they are very well made and very durable. You can also choose the wood if you like. For $10,000 you can have a perfectly suspended table with vacuum clamping, a magnetic thrust bearing, Top notch speed control and a dust cover to boot. Many of these feathers are available in less expensive table. 
There are many spring loaded devices on the market. I the dealer does not ask you for the weight of the table as it plays with recodes an clamps, forget it, move on. The springs have to be tuned to the weight of the turntable and you always go with the lightest spring that will work. 3 Hz. That is what you are looking for. Then you can kiss foot fall problems goodbye.

I would do some homework on damping properties of different materials. There is a name for it, which I forget. You can use two different materials with a damping material in between. Or look at the plinth of the VPI Prime Signature - looks like its aluminum in between two other materials. 

I to live in a very old house with bouncy floors.In my secondary system I have an old Sota on a walnut turntable platform that utilizes rubber balls. When someone walks into this room the stylus  skips. In my main system I have a VPI Classic 3 on a 4 inch thick maple butcher block platform with 4 rubber and cork anti vibration pads. I never have any skipping and can even rap on the rack without any issues. The vibration pads are the same ones that are used in the HVAC industry. These pads are very inexpensive and you will find that the same pads are being sold under some audiophile brand names priced at 10 times their actual cost!