Medium bindings are designed for average adult boots, typically fitting US Men's 8-10 or Women's 9-11. Since you're a men's 9, you're right in the sweet spot for medium, which is the most common binding size and provides the best fit for mid-range boots.
That said, always check the specific brand's size chart before buying—sizing ranges vary between manufacturers. A men's 9 in one brand might sit at the top of medium, while another might place it at the bottom of large.
Also consider your boot's bulk. If you ride with a thick-soled or particularly bulky boot, you might get a more comfortable fit by sizing up to large. Properly sized bindings should grip your boot securely with straps that reach without being maxed out, and your boot should sit flush in the heel cup without overhanging the baseplate.