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You will need velocity for expansion so I would go with super sonic. Something like Barnes tax-x. It's solid copper with a black polymer tip.
Supersonic will expand the most with regular bullets. There are bullet types designed to expand at lower Subsonic velocities that would be the best to limit over penetration in a self defense scenario. Hornady makes a very good loading specific for this purpose : https://www.hornady.com/ammunition/subsonic#!/
it will depend on Bullet design a bullet that expands reliably at supersonic speed may not expand at sub sonic speeds and a bullet that expands reliably at subsonic speeds would most likely fragment (instead of expanding) at supersonic speeds as long as they will reliably function the saint, for home defense I would most likely go with the Hornady subsonic rounds https://www.hornady.com/ammunition/subsonic#!/