David_Kristoffersson comments on Book Review: Naive Set Theory (MIRI research guide) - Less Wrong
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When I first worked through this book, it didn't result in long-term retention of the material (I'm sure some people will be able to manage, just not me, not without meditating on it much longer than it takes to work through or setting up a spaced repetition system). In that respect, Enderton's Elements of Set Theory worked much better. Enderton's book goes into more detail, giving enough time to exercise intuition about standard proofs. At the same time, it's an easier read, which might be helpful if Halmos's text seems difficult.
Thanks for the tip. Two other books on the subject that seem to be appreciated are Introduction to Set Theory by Karel Hrbacek and Classic Set Theory: For Guided Independent Study by Derek Goldrei.
Edit: math.se weighs in: http://math.stackexchange.com/a/264277/255573