This will also say little in comparison to the breadth of your question.

I would include some of the history of how the notion of limit of a function, $\lim_{x \to a} f(x)$, emerged over time. I was surprised to learn this concept was not present (or at least not clear) in the work of either Newton or Liebnitz. It took another hundred$+$ years for this to reach its modern $\epsilon{-}\delta$ form.

Including the major historical struggles fits in well with your 2nd goal, to convey the "intellectual and aesthetic achievement" of calculus.

This will also say little in comparison to the breadth of your question.

I would include some of the history of how the notion of limit of a function, $\lim_{x \to a} f(x)$, emerged over time. I was surprised to learn this concept was not present (or at least not clear) in the work of either Newton or Liebnitz. It took another hundred$+$ years for this to reach its modern $\epsilon$-$\delta$ form.

Including the major historical struggles fits in well with your 2nd goal, to convey the "intellectual and aesthetic achievement" of calculus.