The Beatles always felt like Broadway show tunes to me. It might be a generational thing, but I was enamored with grittier stuff.
Assuming I understand your meaning of "grit", it's the old "Paul vs. John" conundrum! So skip Magical Mystery Tour and Sgt. Pepper altogether!
Here's my gritty playlist for you - all John - "Twist and Shout", "Money", "Dizzy Miss Lizzie", "She Said She Said", "Revolution", "I'm So Tired", "Come Together", "I Want You (She's So Heavy)", "Dig A Pony".
If you only have time for one song, listen to "Yer Blues". Preferably turned up loud.
Here's a great version of "Yer Blues" with Clapton, Keith Richards and Mitch Mitchell. Is this what you mean by "grit"?
https://www.youtube.com/watch?v=Iuy-10Ejck4
Or, skip The Beatles and go right to Lennon's first solo album, "John Lennon/Plastic Ono Band". Just him, his guitar, bass and drums. True grit.
walrus