If someone asked me "I want to watch/know more about DC, where should I start?" or "Where can I watch Superman slap someone around?" or "Who is Batman?" I would tell them to watch the DCAU. No ifs buts or maybes.
Starting with Batman: TAS you have what I would call the best standalone Batman material, period. With the fantastic voice work of Kevin Conroy laying down the chops of Batman (when I read or think Batman, he is who I hear) and Mark Hamill voicing Joker and the rest of the supporting cast, followed up with complex but easy to follow story lines and it's fantastic gothic noir artwork, you get an unbelievable cartoon.
Following on from that, you get my favourite of the series which is Superman: TAS. Move over Christopher Reeve and Henry Cavill, because this is Superman. It's charming, it's complex, it's fun, it's beautiful to watch and it stands out even today just like B:TAS. It has a mix of old looking technology mixed in with futuristic but believable technology, and bright artwork that just brings Metropolis to life. (Seriously DC and WB, why haven't you remastered this in Blu Ray like the rest? You are sleeping on Superman and it breaks my heart...)
Then you have a few other gems like Static Shock and Batman Beyond which are worth a watch if they interest you.
And then you get Justice League and Justice League Unlimited. I love Marvel (Spidey is my main man!) but please step aside MCU, this is how you do Superhero storylines. It throws everything the previous series had and mixes it all together with the added bonus of the other members of the Justice League. It's brilliant and it works.
I'm not going to write anything more about these two shows, because if you are here and reading this, it means you are slightly interested to begin with and you shouldn't be reading me dribbling on, you should be watching the shows! Seriously just go do it. I mean it. Do it.