Reddit reviews Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic

Since you definitely have plenty of philosophical background, I think you could handle a very abbreviated run through logic, like Lemmon's textbook.

Then, for the more advanced (read: fun) stuff, I really like the Beall and van Fraassen textbook (and not just because van Fraassen was an instructor of mine [actually, he taught me the content of this book, among other things (too many nested parentheses, I shouldn't be allowed to post while drinking)]).

Godel, Escher, Bach is an entertaining read that will cover a lot of the basics or first order logic in an accessible way. Beyond that it gets difficult. A friend of mine, who is a practicing logician, once thought about writing a decent logic textbook while she was finishing her PhD, but her adviser told her not to until she had tenure somewhere, as people would assume that if she were writing textbooks for undergraduates she wasn't up to doing real logic. Of course the funny thing about that is that he himself, wrote a few logic textbooks. His Possibilities and Paradoxes is a little dense for someone to work through on their own, but with some dedication and work, it can be done.

Peter Suber teaches a class called "Systems Logic," and has a lot of material available online here. Between that and GEB (as it's called), you can get a good feel for what logic is all about.