I am interested in learning some fingerpicking songs. My goals right now are to learn things like: Classical gas, Dust in the wind, nothing else matters, and other things like that. Surfing around the internet has told me that the thumb looks after the "bass strings" (I assume this means the top 3, correct me if wrong), and the index, middle, and ring finger look after the treble strings (one per string). Now with this pattern, does it matter if i anchor my pinky to the guitar? Or is there some reason not to do it like there are arguments for not anchoring with a pick.

Also, what are some songs that are like the 3 mentioned above that sound cool?

You'll be moving your fingers around a bit. If you're playing on strings 2 (B) to 5 (A), you'll put your thumb on the A, your index on the D etc. Experiment and you'll find something that works. If you have to play on 5 strings, it's usually easier to move your thumb from one string to another than with your other fingers.

Opeth has a bunch of good songs - they use a capo, though. Damnation, Still Day Beneath the Sun and Patterns in the Ivy II are my favorites to play.
I'm a communist. Really.
Sultans of Swing by Dire Straits is a great song to boost your fingerstyle speed and accuracy.
Both Benighted and Face of Melinda by Opeth are great songs, as well as the other ones Raziel mentioned.