Titebond's Genuine Hide Glue would be an excellent choice. Hide glues are "stiffer" and harder than are "regular" glues, which exhibit a little "give". I used hide glue when I was working in a cabinet shop, the glue made by pouring dry hide powder (bought in large bags) into a "trough" and adding hot water, mixing the two together and letting it cook overnight. It was a messy, stinky substance, but it's the best glue structurally.
And that's what you want in a plinth---no relative motion between the layers of wood (or whatever) you make the plinth out of. As for the wood, there is nothing better than 18mm 13-ply Baltic Birch Plywood, available in 4' x 8' and 5' x 5' sheets for under $100. Take a look at the details Art Dudley provided in his article in Stereophile from a few years back, on his building of a plinth for his TD-124.