Despite everything, I believe that people are really good at heart.
- Anne Frank
I just like to throw quotes in every now and then. I'm actually going to go with the answer of "both and neither". This kind of goes back to the old nature versus nurture argument, I think. Inherently, we all possess certain qualities, but every experience - every day, every person we meet and everything we go through shapes and defines who we ultimately become, and we I believe we do have some control over it.
I'll take myself as an example. I try to do right by most everyone. I don't like to drink and drive - because I might hurt somebody else. I'm nice to everyone unless they give me reason not to be. I don't hurt animals or other people. But sometimes I want to. I have horrible, sometimes murderous thoughts and rage all the time. A lot of people do. I cannot, and will not act on it if I wish to live a (somewhat) free existence. Some people can't control their anger, their hatred, and their general awfulness.
As for selfishness, we all possess some degree of selfishness. It's hardwired - the instinct to survive. I don't see why selfishness as a human quality has a negative social stigma. None of us can absolve ourselves of it completely and pass judgment on another whilst being completely in the "right", so to speak.