[vitriol83]

The difficulty with learning 'modern' algebraic geometry is not only is it very dense and general, but that means the original motivation can become lost.

So I think understanding Weil conjectures are key for modern algebraic geometry. And it's always easier to understand algebraic curves (algebraic geometry with dimension 1) and their connection to Riemann surfaces (algebraic curves over the complex numbers with analytic rather then algebraic structure), as they provide motivation for many of the results and constructions.

A good introduction to Algebraic Curves and the Weil conjectures I've found is following

https://math.mit.edu/~poonen/papers/curves.pdf

For general algebraic geometry, JS Milne's notes are rather good

https://www.jmilne.org/math/CourseNotes/ag.html

and for an introduction to commutative algebra Atiyah-Macdonald's book is great.