When I first started learning the guitar I would always enjoy strumming Beatles tunes, they were good for singalong songs.
I've just about got to the stage where I can play Mc Cartney's "Blackbird" up to speed. It's amazing to think that piece was written in a day, ok to some it may be a simple song but I think it's superb for running up and down the fretboard and for a basic picking exercise and It sounds impressive. Got to admit I have yet to master being able to sing along to it, but there again my voice has never been one of my strong points.