I would start with something like Elementary Analysis: The Theory of Calculus, and work from there. You'll eventually arrive at the same place -- Calculus but from a much stronger mathematical foundation.
They do focus on complex problem solving, which is equally important. The key value-add of AoPS are interesting, often beautiful examples and problems.
However, they don't do proofs or formalism much. They don't do applications or show what math is useful for. And they completely, totally, and universally screw up units (you'll have problems trying to equate a length with an area and similar; that's true of their classes as well, and RSM is similar).
I don't think there's a one-stop-shop for math, though, which does everything right. AoPS is at the peak of their particular game (which is right in the name: problem-solving).
That's best complemented by:
- Something which does data, applications, visualizations, and storytelling well.
- Something which does early exposure / surface learning well
- Something which is more formal and rigorous in terms of proofs and derivations
- Something which touches on a broad set of interesting topics (graph theory, oddball parts of geometry, etc.)
- In 2024, I would add something which does computational mathematics well
Nothing I know of does all those well in a one-stop-shop.
It's confusing because that title is also the name of the publisher / website of the series of the books I'm reading.