Found it! Here are the first books bare in mind that this is all before the Nu-52! (so it was all retconned, at least the stuff I care about!) so it won't necessarily help you jump in to the current stuff.
Pre-Robin/First Years:
Batman: Year One. Standard stuff and probably the only Frank Miller on the list. Movie has a good scene with Selina in which their fight is a draw rather than Bruce winning as in the comic.
Alternative origin story: Batman: Mask of the Phantasm. My head canon includes parts of both.
Batman: The Man Who Laughs. If you want a decent introduction to the Joker.
Batman: Snow. Mostly here because it's pretty.
Somewhere here Bruce confronts Joe Chill and pretty much drives him to suicide. (As seen in Grant Morrison's run.)
The Long Halloween. Introduction to the world, villains and one of my faves: Two-Face.
Alternative: BTAS Two-Face Part 1 and 2.
Arkham Asylum A Serious House on Serious Earth. Forget exactly when this takes place but I think it's weird/interesting/different enough despite it's flaws.
The main thing here is that Bruce is on a downward spiral despite everything he's doing for the city. (I also don't care for the whole "Batman makes Gotham worse!" interpretation. I think he makes it different, but probably a net good and he is NOT responsible for the creation of his villains. Except Jason.)
Dick Grasyon as Robin
Dark Victory. Pretty much The Long Halloween retold but introduces Dick so it's worth it. A bit darker take on Dick's introduction.
Alternative/Accompanying: BTAS Robin's Reckoning Part 1 and 2.
Alternative/Accompanying: Batman: Legends Of The Dark Knight #100
Robin: Year One. One of my favorite Batman stories.
Batgirl: Year One. Barbara's origin story.
Of course, there's a bunch of campy stories from before Crisis on Infinite Earths with Dick as Robin. As well as some "flashbacks" that I'm forgetting. So I'd have to go through those again and pick out some standouts for Dick growing up and going to college and then becoming Nightwing. Crosses over with Teen Titans.
Jason as Robin
This is a bit hard because Jason became Robin just as they did the first reboot so you have some weird stories where he's a Dick clone.
Whatever issue his origin story was in.
Alternative: Nightwing: Year One. There's some stuff I don't like about it, some stuff I do.
Whenever he kills that rapist.
A Death in the Family. Really needs to be rewritten because the actual comic is bad but I like some of the stuff that is left out of the flashbacks in the Under the Red Hood movie. (Like his mum finding him and betraying him. That shit's important.)
There's another retelling of Jason's death that I absolutely adore but I always forget the issue. It's some random thing. I need to find it again.
Tim as Robin
A Lonely Place of Dying. Tim's introduction.
Oracle: Year One. Barbara becoming Oracle.
Totally agree. I don't think Bruce ever really expected to be a dad and went through a lot of growing pains with the first kid. I put him as being at least 25 but probably a bit older when he first takes in Dick.
And also agree about stuff like The Killing Joke. Arkham Asylum I think is interesting because of its style and general narrative style but the best stories are the random ones with his kids for sure. :3 I just binge read through every Robin, Nightwing, and Batgirl issue in high school so I can't recall actual issue numbers and there aren't that many trade paperbacks anyways.