I would recommend Rebirth its a great Point to start (I started there too). Just pick a Character you like and read their Rebirth Run (If They have one)
Or try a Year 1 story, the modern DCU was born from Crisis on Infinite Earths.
You start with a character you like, and read some of their best stories. We can help if you know which character, team or genre you want to start with.
Don't worry about getting the weekly comics or "staying current". That's a waste of money.
Since you've tagged Superman and Batman, here are my recommendations for them.
Superman:
If you think you'd like the campy bronze/silver age Superman stories better than the modern, more grounded takes on the character, you might want to talk to Mektonz since that's his area of expertise.
I personally recommend the following stories:
Superman: Man of Steel by John Byrne
Superman For All Seasons by Jeph Loeb and Tim Sale
Superman: Peace on Earth by Paul Dini and Alex Ross
Superman: Kryptonite by Darwyn Cooke and Tim Sale
Superman's Pal Jimmy Olsen by Jack Kirby
Death of Superman Saga
Superman: Red Son (Out of continuity)
Superman: American Alien (Out of continuity)
Kingdom Come (But you might appreciate it better once you've read a bunch of other DC stuff.)
Batman:
Here's a list of the best starting points from each era of Batman's history. I'd recommend trying these and looking for follow ups to the one you like best.
Golden Age: Batman: The Golden Age Book One
Silver Age: (there aren't really any good Silver Age Batman collections yet)
Bronze Age: Batman: Tales of the Demon or Tales of the Batman: Steve Englehart
Pre-crisis 80s: Tales of the Batman: Gerry Conway
Post-Crisis 80s: Batman: The Caped Crusader Vol. 1 or Batman: Dark Knight Detective Vol. 1
90s: Batman: The Knightfall Saga
2000s: Batman: No Man's Land
2010s: Batman by Snyder and Capullo
For Batman, the starter materials I usually recommend is Year One and Hush; Year One is the main origin story, and Hush is a guided tour past his friends and foes. Yoiu don't need to start with the Golden Age to learn about him.
After Year One, you can also read The Long Halloween (and Dark Victory) but they're drawn by Tim Sale. Like the Superman recommends by him above, his art is a bit out of the ordinary and may feel strange to new readers.
Thanks a lot guys
To any new reader I suggest
-Superman: Up in the Sky
-Batman: Universe
-Wonder Woman Vol. 1: The Just War
The first two stories are standalone, and doesn't branch out anywhere else which I feel is a good start for new readers
For the Wonder Woman recommendation, it does have two other installments, volumes 2 and 3
What do you think?