Anybody who remotely takes category theory seriously should have Aluffi's book, even if s/he chooses to learn from another book. There isn't really anything that compares in terms of its comprehensive coverage of abstraction at the basic level, and you'll eventually need something like it.

I simply love Moore & Merten's "The Nature of Computation"; it's probably the only book for the absolute (but mathematically-minded) beginner about the theory of computation that manages to be incredibly captivating and lucid (while also covering a significant chunk of material).