I know this question has probably been asked before but I've never really found a suitable definate answer. At the moment I'm studying algebra II and trig. Can someone tell me the best or most logical path to take in order to end up studying quantum mechanics?

This is the path I imagine: Algebra II > Trig > Calculus > ? > ? > ?

I know math is a huge field but I want to take the best route, the best modules which will give me the greatest chance at tackling quantum mechanics. I'm studying at home by myself. If you could recommend a book relavent to the topic at hand that would be great.

Also if you know of anything in particular within a certain field that would be perfect. I'm looking for advice from people who actually study or have studied quantum mechanics. Thanks.