Self Teaching Math for HS Research

High school freshman taking AP Precalc and AP Stats, and I want to get to the point of being able to do applied maths research (maybe in optimization, although I’m not really sure what that is). I know I can get a professor to help me do the actual research bc I’m a part of my school’s research club which has a network of local professors in many fields.

ChatGPT suggested I do the following:

-learn calculus

-learn multi variable calculus

-learn linear algebra

-look into optimization basics and proofs and start reading some papers

Does anybody have tips on if this is a correct timeline, and how to go about actually learning this? I was thinking Khan Academy for calculus, and maybe MIT OCW for a few others. I know this is a very ambitious goal but even if I don’t end up doing good research it would still be like a fun hobby and still be very useful.

Thanks!