Review of Neon Genesis Evangelion
I have been on both sides of the debate surrounding Neon Genesis Evangelion. When I watched it as a youth on Toonami, I thought it was grotesque and the characters were terrible. I watched it again as an adult and saw the thematic elements at work. I still am convinced it's a great anime, though I've also heard it described as the second coming and heard people rail on it for having whiny characters. The first and absolutely most vital piece of advice I can give you is not to self-insert or expect a heroic character out of the nominal protagonist, Shinji Ikari. When you understandthat Shinji is a little shit, you can focus on how his frailties affect his role in the story, which is also a vital state of mind to be in for taking the rest of the cast at more than face value or expectations of what you think characters in their roles should be capable of. Pretty much everyone of note in NGE is carrying a lot of demons and struggle with their roles as the prophecy child, the supportive maternal guardian, the arrogant prodigy, etc.
The show is normally divided by fans into three major sections; an intro section mainly focusing on Shinji's ambivalence about piloting the EVA (think Takumi slowly agreeing to race Keisuke in Initial D), a more pulpy section dubbed the "monster of the week" string of episodes that have a Power Rangers balance of adolescent drama and giant robot fights, and a finale focusing on the deteriorating mental stability of the team and the consummation of all the mysterious, supernatural elements. They're all very interdependent such that you can't really skip parts of them you don't like if you want the payoff of seeing it all come together, though it helps to know both as a warning and an encouragement that the series will change gears a few times.
As I mentioned earlier, everyone has rather intense psychological problems and backstories to explain why. I agree with suggestions that Hideaki Anno's own struggles psychologically give these much more credence and realism. I still don't think I've seen anything in any medium that quite compares in terms of fidelity and attention to detail to the dark side of the psyche. Keep in mind the cast are largely kids, so the actual manifestations of their problems are immature, bratty, and even annoying at times. The same sometimes go for the adults too, as their traumas have kept them from attaining true adult maturity. Alongside the aesthetics, this introspection is the greatest thing NGE has pulling for it.
The visuals themselves are compelling, with gore and religious imagery liberally splattered over it. The music work is great and the cues are consistent in setting you up for the mood of the scene, or in contrast scenes that beg the viewer's attention and assessment will feature little sound work to put the focus on the characters' intimacy and dialog. There are rough edges, as the project had its fair share of money problems, though repeated frames and minimalist, experimental changes to the art style (especially in the last 2 episodes) were money-saving shortcuts that ended up making the work even better than it might have been with a fuller budget to pursue a more conventional, kinetically oriented direction.
All of that said, and the following does not change my opinion that NGE is a very great work of art, do not vivisect Evangelion simply because it is deep and artistic. A lot of choices in the series were picked for impromptu or transparent reasons. Hideaki thought Christian imagery was cool looking, hence it was used. Evangelion was first and foremost a giant robot show in concept simply because they're cool, not to trojan horse in a Freudian psychoanalysis. The show deconstructs a lot of tropes and anime pulp, but at other times it indulges in them. This is all to say that looking for the 4th dimensional connection between all the threads is all well and good and there's enough there to sustain it (as it has been in endless forum debates basically since NGE came out), but one shouldn't let shouting its praises or digging into it distract one from enjoying NGE for the art it is rather than the art we can analyze it into being.
Should you watch it though?
Yes; Get in the fucking robot.