I'd start with Abbey Road and work my way backwards through their catalog.
Abbey Road (Their most modern sounding and probably at this point their most beloved release)
The White Album (which is my personal favorite and by far their most personal in terms of songwriting)
Magical Mystery Tour (not considered as good as their other psychedelic release, Sgt Pepper, but song for song this happens to be one of their most consistent albums, and perhaps of all their albums it features the most well-known material)
Sgt Pepper's Lonely Hearts Club Band (considered by critics to be the seminal record ever released by the band, and probably of the entire rock movement)
Revolver (One of the most astonishing records because it cohesively joins so many different styles. By diehard Beatle-fans, this tends to be the most enjoyed of their albums)
Rubber Soul (This is the Beatles first masterpiece of an album. It features some of their best works and is very serious-minded in comparison to all their other previous works)
Help! (Despite the fact that this album is nowhere nearly as good as any of the previous mentioned, it features The Beatles most famous song, Yesterday, and also the title track which is up there in the ranks of their most famous songs. Other songs on here are great, but there are some lackluster moments here.
Beatles For Sale (This is probably the Beatles least known and least successful album of all their original releases, but it's my favorite of their pre-Rubber Soul releases.)
A Hard Day's Night (The first and only album to feature all Lennon-McCartney songs. John really begins to shine here as a writer)
Let It Be (Ok, here I would get the Beatles' last release. This takes the purchases out of order. It was recorded immediately after The White Album and shares a bit of similarities but it is an uneven work. Half the album is among their best, and half the album is among their worst.)
Past Masters (These are The Beatles singles which didn't appear on an album. As such, this 33 song set contains some of their most well-known material....I Want To Hold Your Hand, Hey Jude, She Loves You, etc. It also contains some lesser known greats like Yes It Is and Old Brown Shoe.)
Please Please Me (This is the Beatles very first album, and in some ways it still remains the most impressive debut by any band in history. The album contains song after great song and at least half the album gets regular radio airplay......it only pales in comparison to The Beatles later, more serious and artistic endeavors, but as a great pop rock album they never surpassed it for pure fun and spirit.)
With The Beatles (Personally, this is the Beatles least enjoyable release. It feels like a carbon copy of Please Please Me and since it was released immediately afterwards I believe they were probably aiming to create a second Please Please Me. It's not nearly as good, but it still is worth investing in if you own all the others above. There are a few standouts here.)
Once you won this.....you will probably want Yellow Submarine which includes 4 songs not included anywhere else.
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