.380's are great little carry guns, but with the ammo demand for .380's the price has gone through the roof. I was talking to my brother-in-law how .380 ammo was more expensive than .45 cal- go figure.
I suggest a 9mm for the simple reasons of; it's a proven round and the ammo is cheap. A cheap price for quality ammo is a big plus at the range during practing.
Everyone has their view on caliber & stopping power.
This is mine...it's all about shot placement. The only way to disable someone really really quickly is with a shot to the heart or central nervous system. A hit anywhere else doesn't guarantee that the person is going down. Despite what you see in movies, any handgun bullet is going to do very little damage as compared to a shotgun or rifle. Any good defensive round (.380 & up IMO) is going to be able to drop someone with a well-placed shot. Another big factor (IMO more important than caliber) is bullet design.