when she fell
Even though we first saw Anna as a human girl, I wonder how much we really know about the person she was. Well, aside from the fact that she was kickass and had amazing strength of character to put up with all the madness she found herself in the middle of.
What is known is that Anna was born in 1985 in north-western Ohio to Rich Milton, a church deacon, and Amy Milton, a housewife. She was an only child because up until Anna came into their lives her parents had been unable to have a child. Unfortunately for them their little bundle of joy was actually a fallen angel, and when she was two and a half Anna began to suffer from what appeared to be psychotic episodes. She was terrified of her dad and would freak out whenever he came near, claiming he wasn't her real father and that her real father was going to come and kill her.
Now if you'll excuse me, I'm going to nerd out for a second here... From a developmental standpoint, it makes sense that it wasn't until after she was two years old that her past life as an angel caused such an episode as children up to the age of two have limited use of memory and thought and are more reflex or object oriented. It's only after the age of two that children begin to think symbolically, so it's only at that point that she would have been able to begin to process all those memories.
Anyways, according to her medical file, she was admitted to hospital in November of 1987, where she underwent therapy that continued for some years (again, according to her file, until at least September of 1994 - or when she would have been around nine years old). After time Anna forgot about ever being an angel, the doctors claimed that the therapy had been a success, and she went on to lead a normal life. What we know is that she was majoring in journalism at university and was not lacking for friends. She also was fairly devout Catholic as her father was a deacon. (Am I the only one who finds it a bit ironic that after running away from God she was raised to be one of his followers?)
But then on September 18th, the day Dean was pulled out of Hell, Anna started hearing angels. It could have been that the magnitude of the event triggered her latent angel abilities to re-emerge, or it could have been that there had been radio silence on Earth up until that point, but it was very clear that she was not a normal human being (or at least it was to the armies of Heaven and Hell, because humans just diagnosed her with schizophrenia and put her in an institution).
Beyond listening in on angels, Anna had the ability to see people possessed by demons for what they truly were, seen first when a demon came after her wearing an orderly at the hospital. The only other time a human had displayed such an ability was when Dean was on the cusp of being dragged into Hell, and could - as Bobby put it - "see Hell's other bitches." In Anna's case, however, it wasn't her proximity to Hell but instead to the divine. Anna also still had some subconscious access to her memories from her life as an angel, even before Pamela brought them back fully through hypnosis. When Castiel and Uriel first came after her she drew a sigil in her own blood to banish them without knowing exactly what it was she was doing.
And this is where it all comes back to Anna kicking ass five ways to Sunday. Despite her family and friends thinking she had lost it, even without her memories of being an angel she accepted what was happening to her with a lot more grace and resolve than many people would be able to. From her actions under extreme circumstances I wouldn't think it a far stretch to say she must have been an awesome human being. I'd also like to think that even though she's back to full angel status the Anna Milton who studied journalism and had human friends and family is still in there. Sadly, being faced with the end of the world she never got the chance to come out...