Batman the Animated Series without a doubt.
http://en.wikipedia.org/wiki/Batman_the_animated_series
Note where it says:
"It is widely regarded by fans as the most iconic modern representation of the Batman character and mythology, and also as the best animated series based on a comic book..."
That pretty much nails it right there.
Not only is it the best adaptation of the Batman ever, it never failed to deliver great plots that weren't simplistic like some other Animated shows *cough* 'The Batman' *cough*. The music was tailor fit for every episode, giving it almost a movie-like soundtrack for every episode, and the art was beautifully rendered, smoothly animated and utilized great artistic shots.
The voices were expertly cast, Kevin Conroy's Batman is just simply amazing in his ability to become the Dark Knight and deliver some really perfect Batman lines with a deep, dark voice that sounds completely natural. Mark Hammill (Yes, Luke Skywalker) is simply magnificent as the Joker, creating in my opinion the best version of the Joker we will ever see. His laugh was dynamic and could be used in a variety of ways, from sinister to joyous to wild.
I could go on forever about this show, because I grew up on it, and for me, this IS Batman. The live action films are great, but nothing has captured the essence of Batman like The Animated Series.
Buy it, you will not regret it.
Batman Beyond is a continuation of Batman the Animated Series, so you can't really compare the two. Its sort of like the next series after B:TAS.
If you're thinking 'The Batman', please stay away. That series is directed by the same animator who did "Jackie Chan Adventures", which should tell you something. The animation is ridiculously simple, the voices sound forced more often than not and the plotlines rarely reach the level of complexity and true artwork I'd come to expect after The Animated Series.