Irishman12,

In addition to those you listed, I suggest you heavily consider picking up "Beatles - Past Masters Volume Two" because it contains brilliant and excellent songs/singles not found on their non-compilation albums (i.e., Rain, Revolution, Hey Jude, Don't Let Me Down, You Know My Name (Look Up the Number).

True, those songs are appear on other compilations, but those other compilations don't have all of them on the same album (so instead of buying 2 or more comp albums you only buy 1).

I'd get those 3 Anthologies last because they contain alternate versions and live performances (interesting and great supplements, but supplements nonetheless).

You're better off getting (in recommended priority):

White Album - not as cohesive as their other albums, but who cares, a lot of brilliant varied tracks sprawled over 2 discs.

Magical Mystery Tour - it contains Strawberry Fields Forever (just might be Lennon's best Beatles song and the best Beatles song overall); some average songs, but it contains 2 or 3 great songs and alot of good ones.

Help! and Hard Day's Night - the 2 best Beatles album before Rubber Soul. I lean towards Help! but that's my opinion; both are magnificent.

Let It Be - an underrated album. The string of 6 songs that open the album is excellent. "Dig a Pony" is underrated, IMO.

Yellow Submarine - I'd get it last

Beatles 1 - compilation album that has "From Me To You" and "She Loves You" (2 timeless early Beatles singles)...AND...the monster single "I Want To Hold Your Hand." It depends if you just want to get this compilation for only those 3 songs b/c the rest of the songs appear in what you have and the above mentioned.