(and they're easy, being Third Eye Blind - Jumper & Nirvana - About A Girl Unplugged)
I'm trying to introduce myself as slowly as possible, to "master" bit by bit techniques and then move on, but having the time of my life at the same time.
A small addition to the sub topic in this thread "Why would you learn another musicians' work?":
All the comments so far have been totally agreeable, but I would like to add that it also depends on the reason for picking up the guitar in the first place. Some people may have as much fun as doing covers as well as writing their own...
But whatever way you look at it, especially if your "teaching yourself" or GT tutorials and the like, following musical examples will dramatically improve learning curves. You also have alot of time to perfect techniques and patterns and then you can move on.
The first 2 song's I've learned were to really compliment existing knowledge of chords from tutorials and GT, and to look closely at strumming patterns and chord changes.
Anyhow.. the song I'm learning now is Creed - One Last Breath, to get used to hammer ons, pull offs and to get my picking hand in synch. 3 days, its going well, its a big curve for me, but deffinatly recomended.