NANANANANANANA - BATMAN!
To your left is a suggested list of Batman media that are all in the same universe. The DCAU (DC Animated Universe) is expansive beyond this point, especially once you concern involving the Justice League and opening up the many, many heroes and villains via that. But if we are to keep this a strictly Batman Animated (Kevin Conroy's Batman) timeline, then those would be the shows you watch.
The Arkham video games also provide a pretty solid representation of Batman's cast and sets, with levied inspiration from the Timmverse/Batman Animated universe.
BATMAN: THE ANIMATED SERIES
Batman: The Animated Series (BTAS) provides, what I feel, is the most comprehesnive and digestible Batman media to date. As the first installment of the Timmverse I have talked about, it does wonders to present itself and its interpretation of the characters. A lot of Timm's work takes from the Burton-Schumacher films and some synthesis between established comic storylines. For example, The Penguin has the appearance of Danny DeVito whilst maintaining a desire for the upper-class and pompous means of carrying himself. 
This is also why Catwoman is blonde in BTAS. Comics were also coversely being inspired off of the animated series. In tandem, the minds of Paul Dini, art of Bruce Timm, and the voice cast of those of Kevin Conroy and Mark Hamill all became a creative powerhouse.
The tone of BTAS allows for both seriousness and whimsy, through the medium of cartooning. Most episodes feel contained, as if it were multiple issues of a comic put together and animated. I believe most of the animated films (especially ones based off comics, like Hush or Year One) achieve this same pace. For a vaguely serialized, Saturday morning cartoon on WB Kids, BTAS earns so much in cultural and artistic impact. I adore the art style as much as the general tone of the series, and can't get enough of the candid interactions found between Gotham's rogues, heroes, and even crossovers between Superman: The Animated Series on occasion. 
BATMAN BEYOND
To talk a little about Batman Beyond on its own, it is a continuation of BTAS set ambigously into the future. Late enough that the 20-30 something year old Bruce Wayne is now in his 60s, maybe 70s. And early enough that Terry McGinnis, also known as Batman Beyond, is in high school. This setting shift allowed for the exploration of a teenage superhero, but with the already well-known mantle and nomer of Batman. Batman Beyond introduces arcs following a main villain, Derek Powers (Blight), who is a quintessential "you made me!" vegence-seeking, vindictive villain character. 
The first season follows the arc between Batman Beyond and Blight as Blight sends hired villains after Batman. Over the season, other conflating villains spawn from both Bruce Wayne's past and the lower levels of Neo Gotham to trouble Terry. It concludes with the also purposefully ambiguous defeat of Blight.
The Batman Beyond: Return of the Joker film does a lot in Terry's favour in developing him as a successor to Batman. He faces off with The Joker, the most impressive villain of Bruce's past. To get into spoilery territory: This film does canonize Joker dying to the hands of Robin, Tim Drake, in a somehwat messy way. Tim, as established before, was given Jason Todd's characteristics and backstory. The Joker Jr kidnapping plot that Tim is put in doesn't help with the Jason erasure. Nonetheless, this film is considered one of the best additions to the Batman Animated universe. In terms of comic runs, Batman Beyond has a few. They're greatly underappreciated, although a new run-- 2023's Neo-Gothic-- is a great addition! In Beyond itself, there are also crossovers again into other DC/WB content, like Static Shock or Justice League Unlimited.
