The textbook Introduction to Quantum Mechanics by David J. Griffiths is extremely popular with physics majors. It's certainly not perfect, but it's my favorite introductory book.
Even an "introductory" QM book still requires linear algebra, multivariable calculus, some Fourier analysis, some partial differential equations, and a tiny bit of probability & statistics. This book does a decent job reviewing that stuff.
My most useful advice to anyone trying to understand QM is: learn abstract linear algebra! In particular, know what an inner product is and why anyone would care about the eigenvalues of a self-adjoint matrix.
Practically all of the axioms of QM are written in the language of Hilbert spaces and linear operators. If you have a solid intuition about those things, then QM is very confusing. If you don't, then QM is hopelessly confusing; it basically looks like mystical numerology.