http://www.feynmanlectures.caltech.edu/III_03.html
"When a particle can reach a given state by two possible routes, the total amplitude for the process is the sum of the amplitudes for the two routes considered separately. In our new notation we write that ⟨x|s⟩both holes open=⟨x|s⟩through 1+⟨x|s⟩through 2. (3.4)"
https://medium.com/the-physics-arxiv-blog/physicists-smash-r...
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—+—+—|—|—+—+—If you go Full Copenhagen, there are no waves, no particles, and no paths. There are only evolving probabilities - which act in unintuitively non-local but predictable ways - and events which appear to sample one possible result from the current state of a probability density.
The probabilities can be composite, which allows for entanglement and superposition.
The probability part is fairly well understood, or at least fairly easy to calculate.
The exact nature of an event/measurement/whatever is still a complete mystery.
But there is nothing in a naive wave/particle/path model that makes it any less mysterious or easier to understand.
I don't think the particle can select a path from a set at the time it's fired. That sounds very much like a local hidden variable, which is more or less strictly ruled out by violations of Bell's inequality. Unless you allow causality to go back in time (in which case, it can make its decision on where to land based on, for instance, how it will eventually be measured). You can do things to the particle (like trying to measure it, or entangling it with other particles and measuring them, etc) which make it seem less and less likely that the particle could have selected a "which-way" as it was fired.
For instance: suppose you put a detector on one of the slits as the particles are "in flight". We know this results in no 'interference pattern' observed. How do the particles know to scramble themselves as soon as the detector is put on? It doesn't seem like a local effect, since all the particles that go through the other slit never interacted with the detector at all and therefore shouldn't have been affected. But they are anyway. So either there's some information being passed back in time along the particles' history, or there's some strange nonlocal effect.