I reckon you should challenge yourself. Playing intermediate songs badly is a great way to get better - you'll feel your progress as you slowly nail the movements better and better.
I would reccomend learning:
New York, New York - Ryan Adams (easy song, great strum)
Fake Plastic Trees - Radiohead (even easier song)
Exit Music for a Film - Radiohead (slightly harder, but great knowledge)
aaand, everything off of Grace by Jeff Buckley. That will get you up to spec pretty quickly on how to use alternate tunings, WITHOUT going all Death frickin metal on us.
