I like to say first 3 seasons of Batman, then Superman, then the rest of Batman, then Justice League, then Batman Beyond, then Justice League unlimited.
Id save the movies until after the shows personally.
Also yes, caped crusader is awesome. As is My Adventures With Superman. They are unrelated but both very good.
If you watch Batman Beyond first, then you should be watching JLU afterward and that would canonically be in order. Technically the Batman Beyond movie is before that episode, so as you watch Batman TAS watch the movies and then batman beyond, watch that movie too. Then you can just watch JLU in order just as it comes.