I want to learn more about classical varieties. How do I proceed?

I was looking for more information on Classical Varieties and what exactly it means. I worked through the wikipedia article - Algebraic variety - Wikipedia, the free encyclopedia, but I do not understand what they are used for.

I have taken calculus, multivariable calculus, linear algebra, ODEs, PDEs, (engineering math background). This sort of math has always been a mystery to me. What are the financial implications of such math? I have little experience in geometry (Is this geometry?) and would like to unravel a bit of the mystery, mostly for curiosity's sake. My goal in this endeavor is to understand a bit more of how collaboration, problem solving, and "engineering" is done in mathematics, as well as learn some interesting things (which I am assuming are not practically useful??)

A little nudging of "start with this" or "This should be at your level" or "Whoah you totally have the wrong idea, look at this" would be great