I do think I’d go with a “Year One”-ish story for the first season. For the villains in general, I’d have him start with the more mundane foes to start with, focusing on organized crime and corrupt corporate and government officials, with a few of the non-super foes such as Catwoman, the Penguin, and the Riddler. Season 2 would start going into “questionable science”, with Harvey Dent having his accident in Episode 2 (of course) and the Joker showing up at the end. Season 3 is where I’d want to start with “rubber science” villains such as Mr. Freeze, Ra’s al Ghul, the second Clayface, Poison Ivy’s toxins, and such, and start introducing some non-Bat heroes like Alan Scott and Jason Blood.
And yeah, Barbara’s and Jason’s incidents would happen almost back to back at the end of a season. And don’t forget Damian Wayne as Robin!
Some of the plots in comics (or the great ones in other adaptations) would get tweaks, of course. For example, I’d want to introduce Harold early in Season 1 (as I note above, he develops many of the Bat-gadgets), and in the story where he was killed in the comics I’d have him end up merely Hurt Real Bad.
The principle of tweaking would also apply to villains. I’d kind of like to make the Penguin into an “underworld fixer,” with an attitude somewhat like Carmine Falcone in Gotham, someone whom Batman tolerates and sometimes uses. He’d even actually help the Bat against folks like serial killers (especially those that target kids), environmental offenders, drug runners, and human traffickers. This is the most extreme “tweaking” that I have in mind, but should give the general idea.
PS: In an episode of Gotham, Alfred makes a passing mention of a gardener with a Japanese name (right after Penguin blows up Azrael). This individual, I think, could be a one-time fellow student from where Bruce learned his martial arts, and left with him. Between him, Harriet’s knife-throwing, and Harold’s inventiveness, anyone trying to invade Wayne Manor and expecting Sasha to be the only resistance could be in for some surprises!