Oh, if you’re willing to use the hot hide glue, even better! I’ve never used Titebond’s Hide Glue, but as it comes pre-made in a bottle, it’s not as "genuine" as the professional, industrial hot stuff I have used. Once that stuff is made, it has to be kept heated in electric pots, or it will fairly quickly be hard as a rock. Once it dries and cures, it is impossible to even dent with a hammer. Regular wood glue is like soft taffy in comparison.
At the hardwood store I went to last week in Portland, they sell versions of Baltic Birch with outer veneers of a number of different woods: maple, walnut, the list went on and on. The drawback of solid hardwood is that it’s grain and fiber structure all run in one direction, without the 90 degree "cross-bracing" provided by plywood. And the solid wood is subject to seasonal expansion and contraction, responding to moisture (humidity) in the air. Warping is not uncommon. Solid hardwoods lack the structural stiffness and damped characteristics of plywood. But any one of them may provide a "flavoring" you find pleasing. You won’t know till you build it, install the table, and listen!