When I think Beatles compression I think of a few things: high ratio with a pretty fast attack, medium release, and lots of transformer coloration from outboard comp. units. In my opinion, everything but the latter is song-dependent and therefore getting those sounds for yr songs would be a more nuanced process, so a stompbox with a transformer would probably be your best bet. Check out the Bogner Harlow, has a Neve wound transformer and definitely accentuates similar "presence" frequencies as I hear on Beatles records.
Give the Tortenmann TK-23 Kompressor a listen. Well worth it. I've gone through two periods of my life which involved "compressor hunt" and this won, hands down. Wonderful, hifi sounding germanium based compressor. Just enough squish and just enough attack. It makes your guitar sound like it's been mastered and pressed to thick vinyl.
A lot of the Beatles tones were direct to desk as well, so I'd be looking at a JHS Colour Box / Cali 76 combo. The original Abbey Road compressor was an EMI RS124 but I'm not aware of a pedal emulation. The Urei 1176 which the Cali 76 is based on is the right era though.
Another vote for the Janglebox, it's what is was made to do. People like to complain about how it isn't as "transparant" as this or that, but it wasn't made to be. It imparts its own flavor on whatever you run through it.
It nails those Beatle/Byrds sounds with a Rickenbacker 12 like no other, just ask Roger McGuinn or Mike Campbell if you happen to run into them(;