Oh, totally "obtain" entire albums rather than songs. It's just as easy and you'll get more variety. Anyway, here's a tip- if you want to discover lots of different types of music, go find some greatest hits/singles collections. By seeing a band's best songs, you can see whether you like them enough to find their entire discography.
Here are a few of my favourite albums you might like to try, and some similar artists:
The Rise and Fall of Ziggy Stardust & the Spiders from Mars by David BowieIt's glam rock from the early 70s, and Bowie's best album. If you like this: T Rex.
Love by The BeatlesIt's pretty much their greatest hits, snazzified. If you like this: Wings, John Lennon, Beach Boys.
Elephant by The White StripesGarage rock. The White Stripes are ace, and this is their best album (but they're all different, so it's worth finding them all). If you like this: the Raconteurs, the Strokes, the Libertines, Arctic Monkeys.
Parallel Lines: Remastered by BlondieNew wave-ish, this album is essentially their greatest hits without the Tide is High. If you like this: the Strokes, Yeah Yeah Yeahs, The Jam, Long Blondes.
Different Class by PulpBritpop. Everyone knows Common People, but this is so much more. If you like this: Blur, the Verve, Oasis, Jarvis (his solo stuff).
The Velvet Underground and Nico by Velvet UndergroundArty Rock. It's music to chill to, really. If you like this: Lou Reed, Nico, Joy Division.
Where the Humans Eat by Willy MasonSinger/songwriter blues-folksy music. If you like this: Bob Dylan, Nick Drake, Vashti Bunyan.
Californication by Red Hot Chili PeppersAmerican Rock. Go for any of their albums really, the newer the album, the more chilled and jazzy. If you like this, you’ll pretty much like the rest of my list
Axis: Bold As Love by Jimi HendrixGuitar-tastic jazzfunk. Nothing else really compares.. but if you like this: Pink Floyd, maybe… RHCP definitely.
Bat Out of Hell by Meat LoafCheese-rock. It's driving music.. it's stadium-OTT music. It's fun. If you like this: Aerosmith, Guns n Roses, Lynard Skynard, Bon Jovi, Queen.
Let It Bleed by Rolling StonesWhite Soul/rock. If you like the more soulful stuff: Later David Bowie, Marianne Faithfull..
Sleeping With Ghosts by PlaceboEmo/goth/whingey rock. But it's still good! Placebo are amazing. If you like this: Depeche Mode, Suede.
Razorlight by RazorlightFaux-indie rock. It actually lives up to the hype, love it! If you like this, check out other modern bands: Kaiser Chiefs, Bloc Party, the Kooks, the Feeling, the Killers.
(What's the Story) Morning Glory by OasisBritrock. It's their best album. Everyone knows Oasis; no frills rock. If you like this: Jet, Black Rebel Motorcycle Club, Kasabian.
You've Come a Long Way Baby by Fatboy SlimDance-y. This album is the 90s. If you like this: Chemical Brothers, Daft Punk, Groove Armada.
OK Computer by RadioheadEmotional atmospheric rock. (I'm sure that's not a real genre). One of the best albums ever released, if you listen to NME or Q. If you like this: Thom Yorke, Muse, Coldplay.
Songs for the Deaf by Queens of the Stone AgeGuitar-fan's-wet-dream-rawk. If you like this: Foo Fighters, Audioslave, System of a Down.
The Fat of the Land by the ProdigyDancey ravey fun. If you like this: Pendulum, Klaxons. And if you like them, go one step further into rock with Enter Shikari. And then find some of The Gossip or Deelight to wind down with
Doolittle by the PixiesGrunge. They inspired Nirvana. But you don't need anyone to tell you to download Nirvana, do you? If you like this: Smashing Pumpkins, Nirvana, Silverchair.
The Man-Machine by KraftwerkElectrotechno fun. Or the 80s in a box. They invented techno. If you like this, go find some synth pop because no one else is Kraftwerk: Soft Cell, Eurythmics, Gary Numan, New Order
The Ramones: Remastered and Expanded by The RamonesEarly American punk. If you like this: Dead Kennedys, Iggy Pop, Iggy and the Stooges, the Clash, the Sex Pistols, the Buzzcocks.
Thriller by Michael JacksonFunky pop. For good times. If you like this, go find some Prince right now. And some Jamiroquai.
The Man Comes Around by Johnny CashA little bit country, but fairly dark and broody. For more dark singing: Jeff Buckley or Ray Lamontagne, or for some light stuff, find some of his earlier Johnny Cash or some Elvis Presley.
Yoshimi Battles the Pink Robots by the Flaming LipsPsychadelic spacey amazing music. With stories! If you like this, go find some Beck, some more Pink Floyd, or go completely spacey with something by the Who.
If you're interested in any of the bands I've mentioned, give me a PM and I'll list some songs for you to get