I suggest getting the platinum box set if you don't have many other versions already.
The manga is not exactly the same as the anime and goes a lot deeper into some details. It's a very good manga.
Don't forget there are multiple extra releases as well, even some who are still in production.
The End of Evangelion
Death and Rebirth
A live-action film
Rebuild of Evangelion
Revival of Evangelion
There are also 2 manga:
Neon Genesis Evangelion (The mains series)
Neon Genesis Evangelion: Angelic Days (only loosely connected to the main story)