DS9 is a very tempting choice, what with the sheer number of characters, choice of Captain (Commander) and the many alien leads, but it would be nothing without the template that TOS set up. Sixties TV stories were more about the stars/lead characters, but just look at the supporting cast and the choices made for important (and even unimportant guest roles)
TOS has the black crewman speaking Swahili (albeit an illusory apparition, but Uhura didn't find the man at all out of place on the Ent) in The Man Trap. You had an interracial/interspecies marriage between Sarek and Amanda. There were many, many supporting roles and speaking parts given to minorities with no emphasis placed on their gender or race, they were simply Starfleet Officers doing their jobs (see the Asian female and Black male security guards in By Any Other Name) and countless other examples that went beyond what was the standard of the time.
The more I think of TOS, the more I see the constant effort on the part of the producers and casting agents to maintain the cultural diversity through subtle yet deliberate choices, designed to provide a glimpse of a positive, prejudice-free society (making throwbacks like Stiles, Cochrane and the comments made by Lincoln that much more telling.)