You need to create a Cell Style. In a Cell Style, you can set Vertical Justification on the Text panel.
Since this panel was never opened, I did not realize Cell Styles and Table Styles existed. Very cool.
One last question, if I may. Are these separately used? For example, can I assign both a cell style and an object style in the same way I can assign both a paragraph style and an object style?
Basically, yes. You can use paragraph styles to style the text, and use those style in Cell Styles. You can use Cell Styles inside Table Styles.
Object styles wouldn't apply to tables because they apply to entire frames. Tables are always inside a text frame.
I'd suggest reading about them in InDesign Help or search for tutorials.