Thanks for reaching out! While your Governor is capable of firing slugs, you may not find it especially accurate with them. That's a heavy projectile for a 2.75" barrel to stabilize.
Your revolver can fire 410 Bore, 45 ACP, and 45 Long Colt. I'm afraid we haven't got any 410 Bore in stock at the moment outside of shot suited for small birds and clay targets. When you can find it I'd recommend some 00 buck shotshells for home defense.
For 45 ACP, I'd highly recommend Federal's HST ammo that's optimized for law enforcement: luckygunner.com/45-acp-230-gr-jhp-hst-federal-law-enforcement-50-rounds. Speer's TMJ ammo will prove excellent for target practice: luckygunner.com/45-acp-230-grain-tmj-fn-lawman-50
For 45 Long Colt, I believe this cowboy ammo by Winchester will give you good, reliable performance: luckygunner.com/winchester-45-long-colt-ammo-for-sale-45lc255lrnwinsx-20. That's a lead round nose bullet which is better suited for self-defense than an FMJ/TMJ as well.