I always considered Evangelion an anime classic you must watch, and that's mostly the reason I watched it. Since I've never seen 'deep' anime's like these, I too easily wrote Shinji off as a stupid character, but I kept watching. It was too much to handle for me when I finished the series. I had to watch reviews/analysis videos because I couldn't comprehend what I had just seen in the series version. The Rebuilds in my eyes are a timeline of how things could have turned out. If you're really motivated to watch the show, start with Evangelion, and the End of Evangelion. If you still want more then continue with the rebuilds.
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The following words are out of my reflection of the show, I wrote it a few days ago, but it's not yet finished: