When they first made Evangelion, they started to get behind schedule on the animation about midway through the series, so started to throw in long speeches with no movement, reuse scenes like all hell, or just throw any other random crap to fill out space. They also didn’t really seem to know how to end it so they just threw in some random psychoanalysis stuff and went, righto, and finished it there.
While this should have made the audience lose interest in the show, instead it made people get more intrigued for what was really going on with the story.
So then Gainax tried to make a movie ending to it, but -again- they got behind animating it and had to throw in random stuff to fill out the whole time. Eventually they released a version that was only the first half of the movie ending with old episodes spliced in to fill it out. Then they finally released the actual movie ending separately, but filled out with various random wonkiness.
So the people kept asking for yet more.
So then Gainax cut out some of the cheesey stuff from the movie and again attached previous episodes from the show to fill it out. No new animation was added.
This finally stopped the madness…for a while.
A couple of years ago, the guy who directed it all to begin with started his own new studio and has been going back through and finishing the animation like he wanted, using 3D and modern techniques. But at the same time, he’s also editing the show down to be shorter and more pointed–more like a miniseries instead of a TV show. I saw the first episode or two of this, and it was definitely improved but I haven’t seen the end. I don’t know whether it will have a new and proper ending, if it will fix one of the old endings, or if it will go absurd in an all new way.
Original TV series: Neon Genesis Evangelion
Original Move Re-Ending First Half: Death and Rebirth
Original Movie Re-Ending: The End of Evangelion
Modified Movie Re-Ending: Revival of Evangelion
New Miniseries Version: Evangelion: 1.0 You Are (Not) Alone, Evangelion: 2.0 You Can (Not) Advance, and 3.0 is still to come (if ever)
Personally, I guess I would recommend watching the original series + The End of Evangelion, or waiting until the Miniseries has completed and been released.