Forget trying to play stuff like Rush and all that. You'll just get frustrated and be tempted to quit. When I started playing, I listened to a lot of older music, some of which has already been mentioned here. Here are some great tunes that rock, but feature relatively simple drum beats (yet they're drum beats that totally help the song have its feel):
1. "Green River" by CCR.
2. "The End Has No End" by The Strokes
3. "Dirty Deeds Done Dirt Cheap" by AC/DC
4. "Seven Nation Army" by The White Stripes
5. "The Weight" by The Band
6. "I Need You" by The Beatles
7. "Heart of Gold" by Neil Young
8. "Sing Sing Sing" by the Benny Goodman Orchestra (featuring Gene Krupa on drums)
9. "Thank You (Falettin' Me Bee Mice Elf Again) by Sly and the Family Stone
10. "Aja" by Steely Dan. That's probably the easiest drum part I could think of.
I'd encourage you to start with early rock and roll like Elvis and Buddy Holly, and even some early country like Hank Williams and Johnny Cash. Also listen to old blues, or even some newer blues. Don't shy away from the slow, "boring" stuff...learning how to play the boring stuff will help your chops grow. Listen to the British Invasion, and the stuff that came out before and after it, like surf music...lots of rockin' tunes with good, basic drum parts all around that time. Listen to funk...James Brown, Sly and the Family Stone, stuff like that. If you dig jazz, I'd encourage you to listen to the early big-band stuff from the 30s and 40s. A lot of the drum parts to those songs are fairly straight-forward (and sometimes not as easy as they sound) and will give you lots of opportunity to learn how to swing.
Also, read about drummers that you admire and find out what their influences were, or even just songs that they like. Then listen to
those artists and learn new things from them.