Ok it wouldn't be the same but here's how I see it.
Pre-Buffy
Angel started off as a spoilt trust fund kid with way too much time on his hands. He is however highly intelligent kid who has an interest in History and due to his elaidic memory, does tend to naturally do well in school.
He also had a taste for women, alcohol, recreational drugs and getting into fights.
His father could be some sort of big wig, who is also part of 'Christian Right' conflicting with Angel's liberal views, especially as he knows that his father has indulged in his fair share of immoral behaviour. His father in turn chatises his behaviour, however there is a part of Angel who wants his father's approval.
Angel is however close to his little sister and would do anything for her.
In school he's pretty popular but ultimately finds his peers boring sheep, including the girls. He's always wanted to find someone, exciting and interesting, doesn't stop him from sleeping with them though.
He manages to get into college. I could see him studying History or Art. Anyway, what a suprise, he parties hard, sleeps with girls and gets drunk. Meets a prostitute/junkie called Darla. Cue a life of violence, harder drugs and getting kicked out of college. This leads him to get cut off, so he leads a life of crime to feed his habit. He gets a call from his sister saying that strange 'people' are harrassing the neighborhood and it's freaking her out. Angel of course ignores it and carries on down this dark path.
He does in a way fall for Darla but cannot seperate his feelings from the drug induced 'bliss' he feels most nights. He also discovers the world of vampire bite dens etc. Darla, however mysteriously disappears and is presumed dead. He also learns his family was killed. He investigates and realises (not unlike Justine) it was vampires.
This puts him at a crossroads. He can either continue to deal with his pain and guilt they way he knows how or he can become somone. He chooses drugs and violence, that is until a benevolent demon pulls him out of the gutter, helps him to refine his fighting skills, and sharpens his knowledge of the demon world. He then shows him a girl, a Slayer who can give him meaning to his existence. For the first time ever, Angel falls in love.
BTVS
Angel and Buffy meet, fall in love, everything is hunky dory. He sees Darla again, now a vampire who he manages to kill. Unfortunately, this is not before she drugs him bringing out the inner struggle and he relapses. So along with demons, vampires and various apocalypses, Buffy has to deal with her junkie boyfriend.
After a drunken suicide attempt by Angel, Jenny Calender dies tragically. Angel then spends what seems like 100 years in a hell dimension, other known as rehab.
When he gets clean, he realises he isn't right for Buffy who still believes they can make it work.
ATS
Angel uses his knowledge of what the benevolent demon taught him and also the skills he's learnt on the street to fight demons in LA. Using technology, street smarts and short term mystical compounds, he is able to fight vampires square off against not so nice humans, saving souls in the process.
He's fighting for revenge and redemption for his dark past. Will he ever find the vampire who killed his family? Could it be a certain blond haired vampire? And how will he feel if said vampire is now macking on his girl?
Ultimately Angel starts helping on an advisory capacity, leaving the main demon fighting to his newly aquired friends. Etc, etc.
In short, I can only really imagine it with Angel as a vampire, this is about as close as I could get. 🙁.