Batgirl: Year One? Eh. It's not all that (I own it). Although Chuck Dixon can be a good writer, the take on Batgirl in this was less than impressive. It starts off strong and then degenerates into a by the numbers miniseries. We have corny villains (who could be cool in the right hands) like Killer Moth and a shoddy explanation for why Babs becomes Batgirl. It's only worth the attention of rabid fans (which I used to be).
Must reads for The Batman:
The Killing Joke: Many consider this to be the ultimate Joker story. While I don't agree with that assessment, I do think that it showcases the relationship The Batman and The Joker share. It's a powerful graphic novel written by Alan Moore and illustrated by Brian Bolland. Highly, highly recommended.
A Death in the Family: I consider this to be the best Joker story because, more than any other such story, it perfectly showcases how evil he is (only Miller gets it better). It also features one of the best ends of any iconic character.
The Long Halloween: Although Jeph Loeb's written a lot of stupid garbage over the past few years (particularly bringing back Supergirl and Krypto), this is one of the best miniseries associated with The Dark Knight. It serves as a retcon to the week Batman: Year Two, following on the heels of Batman: Year One by showing what happens with the Falcone Crime Family and how Harvey Dent devolves and transforms into Two-Face.
Dark Victory: A sequel to The Long Halloween, although this is somewhat by the numbers, it's still a fun read.
A warning about Loeb. Although a lot of people consider him to be a great writer, he really isn't. Much of his dialogue is riddled with cliche and taken straight from rather well known movies and books... At least in his Batman books.
Son of the Demon: Although I was never a huge fan of Mike Barr, this is a pretty good story that features Ra's Al Ghul and Talia. It's become something of an... elseworlds story due to the last few panels, but it's not a bad read.
Arkham Asylum: One of the most artistic (and disturbing) graphic novels, this was hailed waaay back as the "sequel" to The Killing Joke... While I don't agree with that perspective, it's hard to argue how intense this book it. It features many of The Batman's most deranged villains and their existence in Arkham and the possibility that The Batman should be there as well. One of Grant Morrison's first forays with the character (and much different than his later uses of the character in JLA).
No Man's Land: This massive story arc that encompassed most of The Batman titles can be bought in trade format. It features most the Dark Knight's greatest foes as well as other non-Bat Villains. I won't give away the plot or some of the surprises, but the best stories were written by Greg Rucka, arguably the best Bat-writer of the past seven years or so.
Knightfall/Knightsend: Thes two mega arcs debut in the 90s and heralded the entrance of Bane. It resulted in the replacement of Bruce Wayne with another characater as the Batman (the lower case "t" is intentional). Far more violent than the real Batman, this replacement was exactly what many fans had been asking for for years. They got what they wanted and then realized that this adjustment was not the character they had come to love... which I think was the point of the series and shut people up (for a while) about Batman not being tough enough. These two arcs are available in trade format. If you want to really appreciate them, you may want to fine a book I think was called The Sword of Azrael that served as a kind of prequel. A kind of sequel to Knightsend was Contagion.
I would also strongly recommend: The Greatest Batman Stories Ever Told, The Greatest Joker Stories Ever Told, and The Greatest Batman Stories Ever Told II (featuring The Catwoman and The Penguin). The older versions if you can get them as the reissues seem to be missing some great stories. If you want to move beyond just Batman comics, I would also recommend Kingdom Come, arguably the best super hero comic book series ever if you pay attention to what's going on in the text (yes, that includes The Dark Knight Returns and Year One, which I love dearly, but do not have a strong intertextual relationship to the business of comic book creation like KC does).
I would also recommend the earliest Batman and Dark Knight Archives if you're interested in the historic development of the character since his first appearance in 1939.
I haven't collected in the past three years, so I have no idea what's going on now... Aside from the apparent (and idiotic) return of Jason Todd. I did collect the Hush storyline. Although the art was gorgeous (Jim Lee) and some of the stuff with Superman and Catwoman is cool, the story is a hackjob. The whole idea of Superman and Batman being best buddies is so antithetical to the characters that it made me sick to my stomach. And now two more villains know his secret identity... In many ways, Loeb and others who cling to the nonsenes of Silver Age material are responsible for a decline in quality storytelling across the DCU.
As for the new cartoon, The Batman, although the animation is smooth and generally very well done, many of the adaptations to the Bat-mythos are poorly conceived... At least when compared to the work done in Batman: The Animated Series (by far the best adaptation of the character beyond the comics). Someone mentioned that this show is blatantly a dual-marketing effort as in virtually ever episode, Bats has to wear a new costume, use a new kind of techology, or some such nonsense to defeat his opponents. If you can afford it, I would recommend buying the three volumes of Batman: The Animated Series, Batman: Mask of the Phantasm, Batman Beyond: Return of The Joker (if nothing else for the great flashback that features the "final" confrontation between the Dark Knight and The Clown Prince of Crime), and The Batman/Superman Movie: World's Finest. These are the best Batman adaptations. Period.
Hope this helps.