Start with Rubber Soul and Revolver and then check out Sgt Peppers and The White Album.
Rubber Soul was inspired by their meeting with Dylan so it has a folk Rock feel To it. Revolver is where they started becoming Psychedelic. Sgt Peppers is were they started with Studio recording techniques to get the sounds they wanted and The White Album is were the started coming apart at the seams and the songs are more individuals than the band.
Rubber Soul - "In My Life"
http://www.youtube.com/watch?v=-ZpVxLjqXPE
Rubber Soul - No Where Man
http://www.youtube.com/watch?v=i5PSN01GzWE
Revolver - Eleanor Rigby
http://www.youtube.com/watch?v=xajQUEPXRyg
Revolver - Tomorrow Never Knows - Psychedelic to the core
http://www.youtube.com/watch?v=6a3NcwfOBzQ
Sgt Peppers - A Day In The Life
http://www.youtube.com/watch?v=fZ2AoCUFsjY
Sgt Peppers - Within Without You
http://www.youtube.com/watch?v=p4G2RlBKbrM
The White Album - really named just "The Beatles" - Yer Blues
http://www.youtube.com/watch?v=sHqvN5YO9wY
The White Album - Glass Onion
http://www.youtube.com/watch?v=He2EZ6-VOOk
The Beatles only have two live albums.
Live At The Hollywood Bowl can only be found used on vinyl.
Live at the BBC which is really a live Radio Show,