To me, the place to start would be the first four chapters of Eisberg and Resnick. I don't think Griffiths, Shankar, and Sakurai really motivate QM properly. E&R give a lot of historical background, experiments that contradicted classical models, etc. I feel that one needs to convince oneself that classical physics had to be modified, to reconcile the theory with these experiments.
If you don't like E&R, Ch. 1-2 of Messiah work well for the same purpose.
Griffiths has no motivation at all, just drops the Schrödinger equation on page 1. This is incredibly unsatisfying, and honestly, readers should feel insulted. Even though the SE can't be "derived," there are arguments by analogy, physical reasons that it is what it is. (For an extreme example, the most convincing argument to me is by analogy to the wave optics -> geometric optics limit, using the Hamilton-Jacobi equation.) Nevertheless, once a reader is convinced about the Schrödinger equation, the rest of the book reads nicely, although it feels like "quantum lite" most of the time.
After Griffiths (or concurrently), go with Shankar. It really goes in depth, and develops your mathematical skills. Chapter 1 is the best treatment of linear algebra for QM that I've seen. I'm not a fan of how the path integral, berry phase, landau levels, etc. are thrown in as an afterthought in chapter 21, but the rest of the book was fun.
Finally, read Sakurai. It fills in a lot of holes that the other books leave, and approaches the rest from an alternative, more streamlined point of view. I particularly like how Schrödinger's equation is arrived at from the postulate of unitary time evolution. (Bonus: there's a new edition with an extra chapter on relativistic QM. The new edition leaves out Young tableaux, so make sure to learn that from an alternative source. The previous (red) edition of Sakurai has a treatment, but I really like Greiner QM: Symmetries.)