I would probably focus on evidence. Why you really need evidence to raise any belief, yes any belief and not just those in "scientific" domains, to the point of attention. That absence of evidence really is evidence of absence. The difference between genuine Bayesian evidence and reasoning by the representativeness heuristic. That no amount of clever arguing will help you reach the right answer if you're starting by writing the bottom line, rather than following the winds of evidence.
In my experience, philosophy students learn plenty about formal logic and argumentative fallacies, not so much about good inductive reasoning.
My school has a weekly event on Thursdays where someone can give a 15-25 minute lecture about a topic of their choice during the lunch break. The standard attendance is about 20-30, aged between 14 and 18, and some teachers drop by if the topic is related to their subject. It's heavily interlinked with the philosophy department, in that topics are typically about religion or ethics, so the audience is generally more philosophically informed than average. A good percentage are theists or deists, and there's a very high chance that the subject will be more thoroughly discussed in the philosophy club the day after.
In a previous lecture a few months ago I tried to explain some standard biases, the Map/Territory concepts, Bayes, and generally attempted to compress the core sequences into 25 minutes, which despite a lot of interest from the head of the philosophy department, didn't go as well as I'd hoped for the rest of the audience. The problem was that I tried to close too many inferential gaps in too many areas in too short a timespan, so for this I thought I should take one rationality idea and go into detail. The problem is I don't know which one to choose for maximum impact. I've decided against cryonics because I don't feel confident that I know enough about it.
So what do you think I should talk about for maximum sanity-waterline-raising impact?