Learn QM algebraic formulations and interpretations

An excellent book which does more or less what you ask for is Asher Peres' "Quantum theory:concepts and methods". It starts from the Stern-Gerlach experiments and logical reasoning to develop the basic principles of quantum mechanics. From there, it develops the necessary algebra.

Another interesting book for an approach of the conceptual side of quantum mechanics is "Quantum Paradoxes" by Aharonov and Rohrlich. But to fully appreciate this one, I think you will need to go through a standard curriculum first.

Then, there is "Quantum computation and Quantum Information" by Nielsen and Chuang, which is meant as an introduction to the ideas of QM as applied to information theory for people with an informatics background mostly. So it also starts from an algebraic and conceptual approach.

Anthony Sudbery, Quantum Mechanics.... is an excellent text which emphasises the theory and interpretation rather than the drill problems...in fact he is a mathematician and quantum information theorist and this book is not so useful for someone who needs to bone up on their perturbation theory and get ready for QED, it focuses on what it sounds like you are especially interested in.

For matrix mechanics (mixed with a bit of schrodinger), see the NPTEL Lectures.

For path integrals, see Feynman, Hibbs (and Styer) Quantum Mechanics and Path Integrals.