The idea is to play a Roy who, for the most part, is identical to that of the Canon one, at least by the start of the New 52. A depressed alcoholic who's aiming to take his own life, yet not able to do it himself. He searches out danger, throwing himself into dangerous situations, in the hopes of doing one last bit of good before he gets killed.
The character will be dragged out of this path by his long time, and closest friend, Dick Grayson. As the latter approaches him with a mission that requires his skills. The idea is to write how Roy fights against his vices, how he deals with constantly being the underdog, and how he'll keep himself above water in his lifelong fight against depression.
I'll workout a Timeline sometime soon, but I'll jot down a couple of things that are on my mind for him so far.
Born from Native American ancestry. He was raised by Natives for his first eight years, his mom then moved with him to Star City. His mother was a long time alcoholic and heroine addict, having more step fathers than Roy could ever remember, each of them a bigger bastard than the last.
He took to some petty crime, but always felt like there was more to life than stealing pocket change from people, soon, he began picking fights with the actual criminals, as a teenager he was protecting people. Upon the emergence of the Green Arrow, it inspired Roy, and he, like the Vigilante, began using a bow and arrow, like he had been taught in his childhood.
The Green Arrow would eventually take him in and make him his protégé, his sidekick, his partner. Oliver dubbed him Speedy, and as a 15 year old, he was patrolling the streets of Star City.
He joined the Teen Titans in his late teens, where he became good friends with Dick Grayson, Starfire, Raven and the rest, but when the team eventually went their own ways, he took the streets of Star City again, this time under the guise of Red Arrow. The years of being a vigilante began tearing at him. When he was 20 years old, his mother died from an overdose, supplied by her fourth husband. Upon learning this, Roy broke into the man's house on the night of his mother's funeral and beat him to death in a fit of uncontrollable rage.
He continued as The Red Arrow for another couple of months, while turning to the bottle like his mother had before him, he eventually retired when he couldn't shoot his bow anymore. Going further down into his misery, he traveled the world, performing odd jobs where he could to get enough money to buy another bottle and a warm bed.
Now, in 2017, he's tired of living, life's not for him and armed with cynical wit, an unhealthy dose of apathy and sarcastic outlook on life, he's putting his foot forward to try and put some good into the world as his final act before he leaves it for good.