Here are my recommendations:
Best Batman stories off the top of my head: Year One, Long Halloween, The Killing Joke, Hush, The Court of Owls, R.I.P, Black Mirror, Under the Red Hood, Knightfall, The Dark Knight Returns.
I would read Batman: Year One first and then the rest and then The Dark Knight Returns at the end. I feel like it would feel like a beginning and end if you started with Year One and read any of the stories from above and then ended with The Dark Knight Returns. Also there is an animated Year One movie and a 2 part Dark Knight Returns movies that are stellar.
Best GL stories: Rebirth, Blackest Night, Brightest Day, Secret Origin, Sinestro Corps War, Circle of Fire, Emerald Twilight, Emerald Dawn, Sinestro.
Honestly with GL, Geoff Johns whole run and whatever other work hes done with the character is top notch. And if your interested, Grant Morrison current new run on the character has been absolutely stellar and critically acclaimed.
Best Justice League Stories: Grant Morrisons run( New World Order, Rock of Ages), Tower of Babel, Kingdom Come, Crisis on Infinite Earths, Justice for All, Divided We Fall, Final Crisis.
Tower of Babel was animated into JL: Doom the movie is loosely based on it but its one of DC’s best animated movies.
These are some of my favorites as well as they are some of the most famous and most critically acclaimed stories from Justice League, Batman and Green Lantern.
For Shazam check out Geoff Johns work on it. His 2011 New 52 story was pretty good.