Recommended Stories
Pre-Crisis
“The Million Dollar Debut of Batgirl!” Detective Comics 359
Barbara’s first appearance ever. It’s a bit dated, but it shows Babs as smart, strong, and capable.
“A Bullet for Gordon” Detective Comics 417
A story that showcases Barbara’s relationship with her father.
“The Unmasking of Batgirl”, “Candidate for Danger”, “Batgirl’s Last Case” Detective Comics 422, 423, 424
The storyline where Babs runs for Congress.
“The Invader from Hell” Batman Family 1
A very silly and fun story where Batgirl and Robin fight Benedict Arnold, who is also the devil.
“Doctor Phosphorus is Back!” Batman 311
Batgirl teams up with Batman and saves the day.
“The Assassination of Batgirl” Detective Comics 491 , 492
Batgirl considers hanging up the cowl after an attempt on her life. An excellent story that shows Barbara’s bravery and cleverness.
Post-Crisis
“Flawed Gems” Secret Origin Vol 2 20
Batgirl’s Post-Crisis origin story
The story of Batgirl’s first encounter with the Joker. A one shot released around the premiere of Batman and Robin. It is much better than the movie it promoted.
“Folie a Deux” Legends of the DC Universe 10, 11
Lovely Terry Dodson art, and a good modern take on Barbara’s character.
Most recent Batgirl origin.
Other
An Elseworlds series set in the 1960s where Batgirl is the first superhero in Gotham. Stars a wonderful, fierce Barbara.
A tie-in comic to the DCAU cartoons. It’s fun! And Babs kicks butt.
Another DCAU comic. The story vaguely resembles The Killing Joke, except instead of getting shot, Barbara helps rescue her father.
Collected Editions
Batgirl: The Greatest Stories Ever Told includes Detective 359, Detective 422-424, Batman Family 1, and Legends of the DCU 10-11, amongst other stories. It doesn’t quite live up to it’s name, but it’s a good collection of stories.
Showcase Presents: Batgirl is a larger collection that reprints all of her early adventures in order. It includes her first appearance, “A Bullet for Gordon,” and the Congress storyline.