Since you like the Beatles, give a listen to the Elephant 6 collective. Not a band, but a collective of bands. The members all know each other and collaborate. Not as active now as it was 10 years ago, but there's a bunch of terrific music that should appeal.
One faily well known standout album is "In the Aeroplane Over the Sea," by Neutral Milk Hotel. Given your tastes, I'm 99% sure you'll love it and wonder why the hell you haven't heard of it before. The other album that knocked me flat is "Dusk at Cubist Castle," by the Olivia Tremor Control. An intoxicating blend of pop, psychedelica and experimental rock. You'll probably wonder why it's relatively unknown, too. And check out the rest of Elephant 6 if you like those. The Apples in Stereo, Elf Power, Beulah, Of Montreal, and many others have a lot to offer.
For some sunny pop that's not too deep but infectious and fun, try Jim Noir. You'll probably recognize a few of his tunes that ended up in commercials.
As for classic rock, have you tried "Village Green Preservation Society" by the Kinks? Another largely unrecognized classic - sort of their "Sgt. Pepper's." I also think you'll go nuts over it, then get sorta angry that you haven't heard of it before. That's how I felt when I first heard it.
You might want to broaden your horizons into a little alt.country. I know country doesn't get much love, but the alt.country scene is not what you'd expect. You might enjoy a little Son Volt and Wilco. I'd recommend Son Volt's "Trace" and "Straightaways." Some country, but they also rock. And if the song "Windfall" doesn't make you start wondering if you might be a country fan, I don't know what would. Also try Wilco's three best albums, "Being There," "Summerteeth" and "Yankee Hotel Foxtrot." Being there has an alt.country/southern rock feel sprinkled with experimentation. "Summerteeth" is a glowing pop album in the tradition of ELO (by the way, try ELO, as well) and Brian Wilson, with just a hint of country. "YHF" is a rock album with a fair amount of experimentation.
If alt.country catches your ear, try a little classic country. I'd go for Johnny Cash's "Folsom Prison Blues," "Red Headed Stranger" by Willie Nelson and "Look What Thoughts Will Do," by Lefty Frizzell. Truly good stuff.
Pick up two of the most-loved jazz albums of all time: "Kind of Blue," by Miles Davis and "Time Out" by Dave Brubeck. These have monstrous crossover appeal. Everyone seems to love them.
Finally, try a little classical. Beethoven has a lot of appeal - try his 5th, 6th, 7th, and 9th. Everyone loves those.