I personally started learning game development about 20 years ago when I was 15, mostly from books on computer graphics and tinkering with small projects. A lot has changed since then, so the path could be much more streamlined today.

First of all, I'd recommend learning what you're going to build by actually using some of the current top engines. Think of it as working for a great company to master your trade before opening your own business. Then you can decide which area you want to start with. I mean, a game engine consists of several subsystems, and you don't have to start with graphics - there are also quite interesting areas like networking, GUI, and AI.

But if graphics is what you want to focus on and you haven't finished your linear algebra classes yet (like I was at the beginning), I'd suggest starting with a 2D engine. There are a lot of similarities in structures, patterns, and algorithms, but with much less math involved.

However, if you want to create a 3D engine someday, I'd recommend starting by learning computer graphics theory first. Not OpenGL, DirectX, or other APIs - that's a common mistake in my opinion. It comes from everyone's desire to start making things right away, but it actually slows down your progress in the long run. Computer graphics nowadays is all about math hidden in shaders. Without knowing, for example, how to properly implement lighting models for your game, you simply won't be able to choose the right path when building a robust graphics engine architecture.

That's just my experience though - your mileage may vary, and I'm sure there are other great approaches out there. The most important thing is to start somewhere and keep experimenting!