I would never carry or suggest anyone carry a 380. So my opinion would be no. I carry a 45 and a 357 or 44mag. I personally would not carry a 9mil but if that is as large as you want to go I think its much better then the 380.
As far as ammo goes what ever works best in your gun. FMJ to the latest HP is going to get your point across.
For me the most important factors in a SD weapon/ammo
1 reliability, is it going to go bang every time I pull the trigger.
2 penetration, is the bullet going to do the damage I want it to do
3 accuracy, is the bullet going to hit in the approximate area I point the gun.
the vast majority of modern weapons/ammo will do all 3. A smaller percentage will do them to my standard. A smaller percentage are in my price range. etc etc.
Good luck, I hope ya never have to use whatever you get.