Part 1 on visual and musical style here.
Almost none of the reviews I've read and listened to have accurately characterized Arthur Fleck / Joker in his role as a violent criminal. This is partly because most people came in with hardened preconceptions about the nature of the Joker as a character, but they still should have noticed how different he is in this movie.
First, Joker is not a vigilante a la Taxi Driver or Death Wish. A vigilante targets an entire group of people who represent a collective threat -- pimps, drug dealers, robbers, rapists, etc. For him, any member of that group is interchangeable with the others -- bumping off any pimp, robber, etc. will achieve his goal of stopping crime. Although a vigilante may have been the victim of a specific criminal, he generalizes that relationship to other criminals similar to the original one, seeking collective rather than individual revenge. His targets have not done anything wrong to him -- he sees them as a threat to a wider group that he belongs to, and is acting on behalf of that group.
Joker, by contrast, only hurts people who have already hurt him: the yuppies who attack him unprovoked on the subway, the co-worker who got him in trouble by giving him a gun, his mother for subjecting him to ongoing physical and mental trauma as a child, and the TV show host who sought ratings by humiliating him before the audience.
He spares another co-worker who treated him decently (and says so). Plus he spares Thomas Wayne, who he could have held a grudge against for telling him the brutal truth that his mother was delusional, that he was adopted, and to stay out of his life or else. It turns out that Wayne was the victim of Arthur's mother's delusions, and she has involved him in her delusions, causing him to get told off by Wayne. So rather than pursue a feud, Arthur takes his licks and leaves him alone. Arthur recognized that he himself was in the wrong, albeit from believing his mother's delusions.
Second, Joker is not a nihilist, anarchist, or other figure who believes in no rules, or that the rules don't apply to him, or that violence and destruction is fun and rewarding per se, a la the Joker from Tim Burton and Christopher Nolan. He does not practice indiscriminate and callous violence. He follows fairly common and traditional rules for who you may harm (specific individuals who have already harmed you without provocation, and not those who have done you no harm). The same goes for property crimes -- he does not smash in the windows of random businesses, or blow up buildings of his targets in a propaganda of the deed.
When he says he "doesn't believe" in any of the political protest motives, he does not mean he believes in nothing, but that he does not have collective and larger-purpose motives. It's entirely personal for him, and that is a traditional ethical code (get revenge against the individuals who've wronged you).
And third, Joker is not really a sociopath. He doesn't torture or toy around with his targets like a sadist, he gets right to the point. And again he doesn't choose targets who haven't harmed him, like a sociopath would. He's not a predator, stalker, or hunter. He never tries to force himself on anyone. He does not hold a lowly view of other people in general, nor does he demean them.
And he can sense when he is in the wrong, how the other aggrieved party feels, and does not try to put the blame on them for feeling wronged. We see this not only when he leaves Wayne alone after their confrontation, but also when he's doing his rent-a-clown act at a children's cancer ward and his gun accidentally falls out of his pants and onto the floor, spooking them all.
In fact, a sociopath would only accept a job at a children's cancer ward in order to gain access to them as a child molester or serial killer. During a bus ride, he makes funny faces at a small child in front of him -- not to try to get close enough to harm him, but simply because he's an aspiring performer and wants to make his audience laugh and reward him with smiles. This is echoed later when he approaches young Bruce Wayne -- to make him laugh, not to harm him after getting him to let his guard down.
He is certainly dissociative, suffers from self-aggrandizing delusions, and is socially awkward or cognitively impaired at empathy -- like an autistic person, he can't easily comprehend what others are feeling. But a sociopath is not cognitively impaired -- they can understand what another person is feeling, they just can't emotionally resonate with it. An autistic is clueless, a sociopath is callous.
This makes Arthur more of a pitiful and doomed character out of Steinbeck. Lennie dreams of petting soft rabbits, but his lack of awareness of his own brawny nature leads him into crushing them to death as he pursues this dream. And Arthur dreams of fulfilling his life's mission of making an audience laugh and feel better -- and getting rewarded with laughter and applause -- while his socially autistic nature means he will never be able to read the room and know what the audience would like, so he only ends up making them feel worse, and he only receives distancing reactions from them.
He's not quite so doomed in his quest, though, since he does ultimately receive rapturous applause from the rioting protesters, after he has set an example of striking back at those who have wronged you.
Making this movie an "origin story" is therefore a decision to return to naturalism and various forms of determinism (heredity, upbringing, current class role, etc.). It's not the typical origin story of a villain from comic books, horror movies, or whatever else. Those villains always rise to the level of sociopath, serial killer, nihilist / anarchist, and so on. Because their violence is so extreme, it feels wrong to reduce it to a naturalistic explanation -- Michael Myers became a serial killer because he got bullied at school, or whatever.
But since Fleck / Joker is not that level of a villain, but is a fairly powerless and pitiful figure who is lashing out at those who have already wronged him, it's totally fine to assign him a naturalistic origin story. And his psychology may be abnormal, but it's not inhuman -- so, sure, investigate its origins in his upbringing, his class position, and whatever else. In a twist, we can't explore the role of heredity through his mother (a delusional psychotic) because he's adopted.
But he was adopted by a delusional psychotic, profoundly neglected, beaten to the point of traumatic head injury by the mother's boyfriend, had been institutionalized himself, perhaps a victim of Munchausen Syndrome by proxy (at the hands of his mother), and loaded up on various psychiatric drugs (some of which may be inappropriate and causing iatrogenic harm, if his mother misled the doctors as to her son's condition).
Current circumstances -- dim job prospects, rising crime, urban anomie, austere government policy -- may play a role in other narratives about psychological breakdown and violence, but it's rare to see one focus so much on childhood and parental influences. There's no such investigation in Taxi Driver, any Batman movie, Blue Velvet, Silence of the Lambs, or scores of others. The brief scenes of childhood abuse in Natural Born Killers is a partial exception, but the throwaway exposition tacked on to the end of Psycho does not count as an in-depth narrative investigation. This places Joker more within the mainstream of Gilded Age naturalism than Midcentury existentialism (free will, agency, making your bed and lying in it).
As our material and ideological conditions have returned to those of the Gilded Age -- hyper-competitiveness, laissez-faire economics and morality, Social Darwinism, and widening inequality -- the subjective sense of hopelessness and determinism will re-emerge into the zeitgeist. When society keeps breaking further and further down, the forces of the world feel too over-powering to be stopped. Only when societal breakdown has been tamed -- as during the Midcentury -- do people feel like they have more agency and are not merely molded and tossed around by fate.