I've had this on my mind for quite a while. I would start off with just Tracer responding to Winston's recall. From there we would see Winston struggle to rebuild the foundations that Overwatch was built upon, trying to establish a budget, make preparations, etc.
As the show goes on, more and more ex-Overwatch members start joining the group, helping out with certain missions (Mcree could do some bounty hunting, Tracer could help Torbjorn find stolen blueprints to a weapon he disowned, etc.) As far as character arcs go, focusing on two or three main characters per season and giving the rest mini-arcs could help set the tone for a particular season. (Maybe the 1st season is about Mercy rekindling her passion for battlefield healing after becoming jaded).
Talon is an important adversary, no doubt, but with how many characters and factions there are, making Talon the sole enemy would be wasted potential. Maybe one season has the new Overwatch go through wasteland Australia, the other focuses on Vishkar conspiracies, another deals with the government and what they would do to the new Overwatch. Helps keep the viewer on their toes.
Personally, I think that Overwatch's main theme could be about making lemonade from lemons. If you think about it, the majority of the characters have had their lives fucked in one way or another. (Tracer being temporarily erased from existance, Genji being dead, Rein losing his comrades, Torb's weapons being misused) Good character growth would take advantage of how each character deals with their predicament, and how they improve as a person; or in cases like Reaper, how they become worse.
If I was a decent fanfiction writer maybe I could write some stories about this shit, but I don't know if I have any real creative skill. Just wishful thinking. :I