I really should ask in here before going out and buying things for the sole reason that they have massive robots beating each other up...
Thanks. Added to the list.
Episodes 1-6 may feel a bit slow to you if you've seen
Evangelion 1.11: You Can (Not) Advance (the New Movie Edition retelling of the same events), but things'll speed up once Asuka appears in episode 8.
Episodes 7-19 comprise the "action arc" that is mostly good ol' mecha with lots of hints toward the greater depths of the story, while beginning to get darker toward the end. Episode 16 gives you the first glimpse of the more mindscrewy parts to come. Episode 19 is probably the real
WHAM episode of the series, and the turning point in to the descent arc.
Episode 19 and 20 begin the "descent" arc in which the show gets progressively darker and characters more fucked up. Episodes 25 and 26 become pure introspective mindfuck. (If you find them a not entirely satisfying conclusion, don't worry; it's not the end yet.)
The movie
End of Evangelion concludes the series. There is still debate over whether depicts different events from episodes 25 and 26 (referred to as EoTV by fans, while the two halves of the movie EoE are officially numbered episodes 25' and 26') or if episodes 25 and 26 depict parts of instrumentality not shown in EoE.
Supposedly, the events of EoE were the original intended ending, before budget constraints forced director Hideaki Anno and Gainax to do episodes 25 and 26 as they are in EoTV instead. The next-episode previews (which show unfinished concept art for EoE) support this. Both endings are technically canon. Some of the artwork and text shown during instrumentality in EoE are fan letters received by Gainax in reaction to EoTV (some of which is hate mail regarding their disappointment and anger with the TV ending). Personally, I like EoTV too, but EoE is is an absolute artistic masterpiece.
It is, IMO, the greatest movie of all time. (I understand of course that it certainly won't be to everyone's taste, so I don't mind if you hate it.) But it is certainly the one that has most impacted my own life.
And it's definitely an anime every anime fan should see at some point. It's as deeply impacted all anime that has come after it in the same way
Citizen Kane has impacted live action movies in the US. (The number of Rei Ayanami expies out there is probably the most obvious evidence of this, though a fairly superficial one.)