Neon Genesis Evangelion
Start here. Shinji Ikari is summoned by his estranged father and told to pilot an Evangelion against the Angels. The early stretch plays as a tense monster-of-the-week series and then steadily turns into something far more personal.
⚠ The final two episodes drop the external plot almost entirely for an abstract, internal sequence. This is deliberate, and The End of Evangelion covers the same moment from the outside — do not stop at episode 26.