I'm interested in anything about examining statements, truth and what is a valid argument in the context of a debate.
Feel free to add further suggestions according to the question.
I continually find Tarski's work on formal languages enlightening. In particular, his undefinability theorem continually helps remind me where the limits of formal languages lie. The arguments also tie tightly into First Order Logic, which is a useful topic to grok fully when exploring validity in debates. Most debaters accept First Order Logic as valid, if you can get them to agree on the base axioms you want to use.
Highly related to his work is Godel's Incompleteness Theorems, which are "stronger" than what Tarski looked at because he restricted himself to a smaller subset of languages where more stronger statements could be made.
I then like to link to the Aggripan Trilemma, which shows how long such questions have been explored. These frustrations with provability are not new -- they're millennia old. This also can serve as a neat trampoline to spring into the field of epistemology, the study of knowledge itself. My personal opinion is that, if you're used to thinking in logic and programming terms, epistemology seems like a waste of time until you've gently jostled your preconceptions about just how effective our programming based tools are for managing knowledge. I find those three topics to be very effective at jostling (if perhaps jostling a bit too hard).
From that point, there's some interesting segues into ontology because ontology is quite interesting when you're willing to question everything you know. From that point, you'll certainly know enough about philosophy to know what to ask for at the next fork in the road.