I recommend "Set Theory", by Pinter. It is a very concise book, and if I am not mistaken, it uses basically von Neumann's approach to classes and sets (you asked for NBG class theory). You you will only need to read the relevant (short) chapter there to feel very comfortable with sets and classes. And if you will want to learn about cardinality issues - you'll find it there in concise form.
This is not the book I would reccommend to someone who knows no math and would like to learn set theory, but for you I recommend it.