You mentioned hearing Beatles songs on the radio in the OP. I have to ask what station this is.

Sgt Pepper's is a good album and I agree with your list of "forgettable" songs, but adding 'Within you, without you" to it.
About the 'overplayed' ones,well, it's not a coincidence that some of the best songs in every album are the ones that end up being played the most, because a song will seem overplayed to whoever listens to that station very often, but they expect any number of "new listeners" every day... also perhaps they were the most audience-requested songs of their time.
Back to the main subject, The Beatles best album is, imo, Abbey Road (from their second period -or after they overhauled their style-). From the first period, my favorite albums are Rubber Soul and Help.

Rubber Soul is great!

Personally, I think Being for the Benefit of Mr Kite is dopeee. I did devil sticks to that song in the 3rd grade talent show.

Don't let roscoe hear that. That's an almost ready-made occult conspiracy theory right here.

Sgt. Peppers Lonely Hearts Club Band - one of the most experimental albums, no doubt about it.

Frownland is gonna straight-up murder you.

Forgive him, Frown. He (or she) seems to be new here.

How many times have you heard them?

"Four shiit-kickers from Liverpool", their words not mine. They made more albums in a twelve month period than 99% of bands/artists today make in six years, they were the kind of big that the modern world cant even comprehend. Pressure! They masturbated into the mouth of pressure and laughed all the way through it.Still to this day they're the yard stick that all others are measured by, they've never been surpassed and its looking increasingly unlikely that they ever will be surpassed. They were the greatest songwriters and they made the greatest albums and that's just the way it is. If you don't agree, you're fecking wrong.

I don't have a favourite Fabs album, but for the sake of the thread i'll go with Abbey Road.