I prefer the mono versions almost across the board when it comes to The Beatles. While the stereos sound better from an audiophile perspective, they just don't work musically. The panning ends up being very, very distracting and the music doesn't have the same "oomph" as the mono versions.
That being said, there are some exceptions. Beatles for Sale in stereo is an absolute stunner on the new remaster. The original tube-cut vinyl was legendary, and this new disc comes damn close to it. It really is a fantastic mix and greatly enhances the overall feel of the album. The White Album has to be owned in both versions because some of the mixing and production choices vary wildly on the album. Sometimes, the stereo mixing is done really well, other times it sucks all the life out of the song. Helter Skelter and While My Guitar Gently Weeps are good examples of the later. The new remaster of the stereo mix is a real doozy sound quality wise, though, and is probably the best sounding album of the entire stereo set. You also need the stereo Past Masters for the few songs that aren't on the Mono Masters set, and I'd say many of the songs on the 2nd disc are worth having in stereo as well, especially Hey Jude and The Inner Light.
There are also some stereo mixes which may be worth owning, but I'm not too hot on. A Hard Day's Night isn't bad in stereo, and some of the songs are in fact better in stereo, but some are better in mono. The stereo Sgt Pepper sounds weak after hearing the mono, IMO, but A Day in the Life is probably better in stereo, which may warrant a purchase by itself. I'll have to hear more, but Magical Mystery Tour could also be considered.
To sum it up, I think you need
Mono Box
Beatles for Sale
The White Album
Abbey Road
Let it Be
Past Masters
And I'd probably get these down the road, maybe used or at a discount:
A Hard Day's Night
Sgt. Pepper
Magical Mystery Tour
The packaging on the stereo discs is also really well done. Glossy cardboard, great pictures, and great booklets. I obviously removed the CDs from the little flaps and stuck them in their own slim jewel cases. The mono box, though, is absolutely stunning. We're talking about ultra high quality mini-LP reproductions of the original UK mono pressings. They even come in their own resealable little bags! The book that comes with the mono box is also really nice.