After long deliberation.....if you want an album to pick random songs from, Nonsuch would be my choice. An alternative, and sometimes described as a concept album, (but that is pushing it really) Skylarking really needs listening to as a whole.(was produced by Todd Rundgren.). Its certainly a long way from the early stuff.
Having said that, Mummer, Big Express , Black Sea and Apple Venus 1 are as good. (English Settlement and Oranges and Lemons have a bit of double album syndrome).
So I would give Nonsuch or Skylarking a bash. Hope you find something you like.
I agree there is "dead wood", but you surely can't leave out the eerie, subtle and often neglected Harrison track, "Long, Long, Long", involving only George himself, Ringo, Paul on Hammond organ and Chris Thomas on piano. It is a rather extraordinary piece, starting as a gentle whisper and ending with George's exhausted wail of relief and the unplanned 30 second wine bottle rattle. In the middle 8 he sings of "So many tears I was searching, So many tears I was wasting" and at the end he does seem to have arrived at some sort of mystical conclusion or reconciliation.
More details here:
Here's my selection for a very good single CD (18 tracks, 52 minutes)
Back In The U.S.S.R
The Continuing Story Of Bungalow Bill
While My Guitar Gently Weeps
Happiness Is A Warm Gun
Martha My Dear
I'm So Tired
Mother Nature's Son
Long, Long, Long (Harrison)
Cry Baby Cry
Your list is very interesting, but please shorten it to 15 - it would be most helpful.
UPDATE! I have just followed your link - fascinating. I am going to play Long, long, long a few times now and reflect.
Know your rights - all three of 'em
and here are the results from the expert North west jury ......
I' so tired
Don't pass me by
Everybody's got something
Helter Skelter (just worked out what Siouxsie sioux spent her youth listening to !)
Back in USSR
Why don't we do it in the road