My Arthur backstory, let me show you it
Arthur was born in the US to a family of low/middle income. I'm shaky on the details - I can't decide if he's a middle child or an only child with distant parents, I'm not certain if his parents were divorced while he was a kid, etc etc because in-movie Arthur's familial history is completely irrelevant. The point is, Arthur is very intelligent but his family can't afford to foot his bill to college. To get into the school of his choice he goes through ROTC. I think that Arthur probably wanted to become a lawyer - he loves organization and also twisting the rules to his own ends ('Paradox.' LOL), so it seems like a good career choice.
In any case. ROTC leads to officer training and whatnot and it's towards the end of his undergraduate run that he ends up encountering this new field of 'shared dreaming' via research groups/training programs within the military utilizing this new technology. In some way Arthur first experiences dreamsharing through the military. He loves it, volunteers into the dreamshare as often as possible, starts to study the architecture end of it. He takes a few drafting classes as electives in his final year of college.
He finishes up ROTC and he ends up being called up and into combat in some capacity. Without getting too specific into my ideas of how this occurs, Arthur experiences some trauma that leads to PTSD. (I lean towards special ops.) He's discharged from the military. Arthur goes back home, drifts for a little while, and the military-provided therapy does nothing for him. His parents/mother/siblings barely recognize this man. He estranges his family accidentally.
Somehow he hears of a research study being conducted of dream therapy for PTSD. Arthur volunteers, gets selected, is flown out to Los Angeles and meets Dominic and Malory Cobb, the dreamshare researchers conducting the experiment. Therapy ensues. It's largely successful. Mal thinks Arthur shows promise as a dreamsharer and hires Arthur on as research assistant and adjunct secretary thanks to his enormous organizational talents. Arthur works closely with them for three years. (Arthur is the first one to suggest carrying guns into dreams for clean, not-being-torn-to-pieces-by-angry-subconscious deaths.)
Dom and Mal are 'household' names amongst the dreamsharing community. Their research papers are at the forefront of the field. They particularly like pushing the envelope with deep dreaming. They do interviews with philosophers and psychologists on the nature of lucid dreaming versus reality. (Applicability is something they struggle with.)
Dom and Mal go into limbo one night and when they come back, aged mentally but not physically, Dom and Arthur watch helplessly as Mal spirals downwards. Paradoxically it's during this time that Arthur firmly cements his friendship with Dom. Mal grows distant and finally kills herself, laying her death at Dom's feet.
Dom flees the country. Arthur follows him. It's Arthur that proposes mindcrime extraction, especially branched off of corporate espionage, as a way to keep feasibly in the black: it's lucrative, it will keep Dom in constant worldwide motion (thus making extradition difficult), it will possibly buy his way home someday. Dom waffles, laying low and scraping by. Arthur peruses the business, takes a job with an extractor, and comes back with a paycheck that convinces Dom it's the fastest way home. (It's during this job that he meets Eames. Specifically Eames spends half the extraction appearing as a hot blonde chick and Arthur has some kind of bizarre femme fatale thing going on with her and then he finds out it's Eames. Arthur is Not Pleased. Eames thinks it's hilarious.)
For two years they are a two-man team, taking on forgers and chemists and later architects when they need them. Mal appears in dreams with increasing frequency. Most of the time she pesters Cobb. Sometimes she goes after Arthur. Occasionally she does so violently. (The gist of shade!Mal is this: she is Cobb's guilt over her inception. She is also his guilt over not dying with her. And his guilt for becoming a criminal. In some subconscious way, Cobb blames Arthur for helping keep him anchored, and for his turn into illegitimacy. shade!Mal reacts accordingly.) Arthur keeps on because it's Cobb. This doesn't stop him from picking at Dom. There are two fistfights, only one of them conducted while dreaming.
The Cobol job comes at a particularly low point for them, a string of jobs that were extended by problems with Mal having disrupted the money flow. We all know what happens from there.
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At the end of the story I tend to think that Arthur stayed out of the country, possibly in Paris (which is in no way related to Ariadne's schooling, nope), and I think he continued to extract. I think Cobb stayed out of dreamsharing for a while - and while I do think he went back to it, he probably did so in a professional capacity. While I'm certain they stayed in contact, I waffle as to whether or not Arthur came to join him. (If Cobb later created some kind of legitimate business in dreamsharing, Arthur would absolutely be his business partner. =D) He sees Eames from time to time no matter what end of the business he's in, because Eames is the best at what he does. He'll take any job Saito proposes in a heartbeat. He commissions his compounds from Yusuf, whose compounds put military-grade Somnacin to shame. And I might be almost totally convinced that he and Ariadne lived happily ever after.
My Eames backstory may or may not be next. Or at least me waxing lyrical about his incredible brain.