'About a Girl' by Nirvana
'Day Tripper' by the Beatles
'Fake Tales of San Fransisco' by the Arctic Monkeys
'Wonderful Tonight' by Eric Clapton
'Good Riddance' by Green Day
You can acheieve more or less anything even as a beginner with enough patience. On of the first pieces I learned all the way through was 'Satch Boogie' by Joe Satriani - it has some pretty nasty bits in it and it took me ages murdering it, but I got it eventually. There are also songs like 'Nothing Else Matters', and 'Enter Sandman' by Metallica which has easy intros that you might like to learn so you're playing something recognisable.
Best thing to do IMO is keep your ears open and if something sounds like it isn't mind meltingly fast, give it a try.... :)
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