>>2647First, I agree with most of what you say, though I want to make a case for classical languages like Greek or Latin as the natural means to learn the first three.
As highly inflected languages, to understand Greek or Latin you naturally learn every grammar concept as they all come into play. I have studied Ancient Greek as an adult and it highlighted how inadequate my US public education was with respect to English grammar.
Two, in learning both of these languages, the student is naturally introduced to history, but in the words of great men and those who looked up to the great men of history. There is a reason the founding fathers studied Plutarch and Polybius. There is a reason the Renaissance involved making translations of many of the classics.
Third, these perspectives in history naturally motivate one to study rhetoric, not as a "school subject" as we think of it today, but instead as a natural skill in the art of bringing others in line with your own views. Schools have too much curriculum, so ideally a new frame will narrow down the required areas of study, while simultaneously giving skills that enable them to pursue any interest they acquire.
Hence, I agree that modern mathematics should be the top priority, specifically taught with very high standards and according to the philosophy of V.I. Arnold, where it is grounded in the physical sciences as it was originally. This enables the pursuit of any field of science and engineering subsequently.
The next priority would Ancient Greek and Latin where grammar, rhetoric, history, and literature are all read as a means of learning these languages. Once learned to the standard of an educated 19th century English or German schoolboy, you will be able to engage deeply in most any conversation in the arts, classics, history, or most anything else much better than even modern academics who rely on the same few translations, and even then rarely study the classics.
Beyond these, I see any other subject as electives. Though for my own children I would emphasize physical fitness, and practical engineering through hands on work.