Two questions.

1. Can someone tell me of a good introductory book on set theory? I am looking for something that:
- is intended for pure math majors, not applied. Something like Spivak's Calculus book would be good.
- has proofs
- has problems, preferrably hard ones, not rote "apply the formula" problems
- calculator stuff would be nice, but I don't know how many of those set theory could have

2. Any thoughts on Jerry King's Art of Mathematics?

1. I'd highly recommend Set Theory and Logic by Robert Stoll. I think it meets all your criteria nicely, except the calculator part. I don't see why you'd want a calculator for set theoretic problems. It's also a Dover book, ergo inexpensive.

2. Nope, don't know it.

I second the recommendation of Stoll's book. I can't say whether it's the best to read, but I did enjoy what I've read of it. I have an older edition, but Dover always does a nice job so I'm sure theirs is nice, too.