Here are some links which may interest you comparing frequentist and Bayesian methods:
In a nutshell, the way I have understood it, given a specific set of data, the frequentist believes that there is a true, underlying distribution from which said data was generated. The inability to get the exact parameters is a function of finite sample size. The Bayesian, on the other hand, think that we start with some assumption about the parameters (even if unknowingly) and use the data to refine our opinion about those parameters. Both are trying to develop a model which can explain the observations and make predictions; the difference is in the assumptions (both actual and philosophical). As a pithy, non-rigorous, statement, one can say the frequentist believes that the parameters are fixed and the data is random; the Bayesian believes the data is fixed and the parameters are random. Which is better or preferable? To answer that you have to dig in and realize just what assumptions each entails (e.g. are parameters asymptotically normal?).
Both Bayesian statistics and frequentist statistics are based on probability theory, but I'd say that the former relies more heavily on the theory from the start. On the other hand, surely the concept of a credible interval is more intuitive than that of a confidence interval, once the student has a good understanding of the concept of probability. So, whatever you choose, I advocate first of all strengthening their grasp of probability concepts, with all those examples based on dice, cards, roulette, Monty Hall paradox, etc..
I would choose one approach or the other based on a purely utilitarian approach: are they more likely to study frequentist or Bayesian statistics at school? In my country, they would definitely learn the frequentist framework first (and last: never heard of high school students being taught Bayesian stats, the only chance is either at university or afterwards, by self-study). Maybe in yours it's different. Keep in mind that if they need to deal with NHST (Null Hypothesis Significance Testing), that more naturally arises in the context of frequentist statistics, IMO. Of course you can test hypotheses also in the Bayesian framework, but there are many leading Bayesian statisticians who advocate not using NHST at all, either under the frequentist or the Bayesian framework (for example, Andrew Gelman from Columbia University).
Finally, I don't know about the level of high school students in your country, but in mine it would be really difficult for a student to successfully assimilate (the basics of) probability theory and integral calculus at the same time. So, if you decide to go with Bayesian statistics, I'd really avoid the continuous random variable case, and stick to discrete random variables.
Best Answer
It is not necessary to call it frequentist material, rather material from probability and statistics in general.
Here are some examples of prior knowledge that, in my opinion, would be handy:
The Bayesian paradigm being a subjective one, I am sure others will disagree with or add to this list...