Tolkien, Lewis, Chesterton etc. are a great introduction to the Great Tradition, one of the virtues of which is that you can start anywhere. Obviously you want to go back to the sources which they themselves were drawing on, but one of the reason they are so deeply good for young people is that they don't just introduce you to "big ideas" or philosophy -- they introduce you to durable ways of being human.
Yes, as you pursue your education you'll need to read older things and more technical things, but if you know the benefits of a bath, a pint, a pipe -- if you learn to be a friend, fight courageously, bow the knee to a Queen -- if you can stand in awe at a holy site, memorize the right poems for the right moments, and love something beautiful -- if a student has these things they are well on their way to the true goal of education, which is not simply to produce political actors.
In this sense, Middle Earth and Narnia are the best "base" you're likely to run into in today's world for a humane education. Such a person already has the imaginative categories they need to move into Homer, Dante, St Romanos, or wherever else their studies take them.
So, as educators, instead of complaining that the kids had their imaginations formed in the shire, we should be saying, "And if you liked THAT, you're going to love..."