The LCP is a great carry pistol. I carry a very similar S&W Bodyguard 380 in a DeSantis Nemesis pocket holster. The combination works very well.
I recommend you think about picking up a second gun soon. Get something that is cheaper and more comfortable to shoot. 380 ammunition is pretty expensive, and the thin form of the LCP can be downright painful to shoot for any length of time.
You would be well served to get a 22 soon. They are inexpensive to shoot and very comfortable. That's means more shooting, more fun, and becoming a better shot.
Please stop by the introductions thread and tell us about yourself.