Kneale and Kneale is a definite must. You could read the hundreds of tomes on dialectic, rhetoric, and logic that came before the modern era, or you could just read what they have already digested for you. After that read Sainsbury,
Logical Forms. That will catch you up on modern philosophical logic. Then read Sommer's,
The Logic of Natural Language, to unlearn the nonsense that modern predicate logic has added to (and removed from) traditional formal logic (Sommer's terms).
You can read Clark if you want. I've read his book twice and found it to be outdated and much too cursory for study. Sommer's new term logic will serve you much better. If you're interested in mathematical logic, get Pospesel's
Propositional Logic and
Predicate Logic. You can try Russell and Whitehead,
Principia Mathematica, if you're feeling ambitious. If you want a current spin on Aristotelian logic, read Kreeft's
Socratic Logic. I don't recommend it, though. It's absolutely terrible.
I've got
Biblical Semantic Logic currently sitting on my shelf along with
Validity in Interpretation. I was working on these while trying to formally demonstrate term logic from Scripture. That always and inevitably ends you up at the philosophy of language, which is how I ended up reading Sommers. I'll tell you what, that's about as complicated a subject as it gets. I'm not sure we'll ever figure it out, but the resources I mention above should keep you occupied at least for the next year or so. If you're still hungry for more after that, you're either nuts or have a mind for the topic. I haven't quite decided which end of the spectrum I fit into, yet...
Oh, if you have trouble finding
The Logic of Natural Language for a decent price (it's a textbook, so it runs around $100, normally) you can get a taste of Sommers philosophy through
The Old New Logic, which is a collection of essays on Sommer's reformulation of term logic (which he calls, "term functor logic"). Some of them are complementary, some are not. Good book, all around.
Oh, and W.V.O. Quine is mandatory. His theory of the indeterminacy of translation has to be overcome for there to be a valid proof for the Bible. I'm pretty much convinced there isn't one.
Bah, I could go on and on. The above should suffice for now.
Soli Deo Gloria
Jon