I'm a math professor, who got through most of Rudin as an undergrad. Felt like a form of hazing at the time ;)

In my opinion, Rudin is a great book if you're reading it under the guidance of a good teacher. For self-study, I don't know of any particular alternative to recommend, but I would select something more "talky" -- i.e. which goes more into the background, motivation, and philosophy of the subject.