Everything I now understand about QM I owe to Aaronson and Baez. Some of what I hope to understand eventually I owe to Coecke.
Inventing QM in 1800:
To deal with some measurements, we need something like probabilities. However, probabilistic dynamics have tons of irreversible operations (diffusion, shuffling....). Yet, we believe microscopic physics is time-reversible. Crafting the inverse of irreversible stochastic operations requires "negative probabilities". [Baez]
If you want negative probabilities, the only consistent way is QM (you cannot stop at negative reals, you must go to complex, and then you have duality and so on -- your "probabilities" have become wave-like). [Aaronson]