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I would like to thank you all for the much helpful answers! I have ordered a copy of Introduction to Quantum Mechanics by David Griffiths and will create a self-study plan so I will be able to hopefully finish a few chapters during the summer.
I agree with your point about some high-rated books as terrible introductory textbooks. I bought a general physics book from a local book store last year and found it to be very heavy in mathematics but offered almost no conceptional explanation. Regardless, after a slow one or two pages per day, I truly understood the topics and learned to extract conceptual explanation from mathematical formulae.
I believe you've answered all of my questions and then some. I actually plan to learn basic Fourier analysis along with quantum mechanics, and I may just start QM immediately with the book you recommended. It has positive reviews (frequently mentioning its clarity and simple mathematics) and wouldn't be a large financial loss if I decide to read another instead.
@dmckee: Thanks for making it CW for me. I remember setting that option for subjective questions on other Stack Exchange sites, but for some reason I couldn't find the checkbox.