If you wish to be cross-platform in any way whatsoever, steer clear of WinAPI. WinAPI is less of a graphics API and much more an OS API. OpenGL is cross-platform, but needs an OS-dependent window manager to be useful. WinAPI will only ever work on Windows (also on emulation software like Wine, but results are never guaranteed).
In addition, it is my personal opinion that WinAPI is just plain ugly and much less fun to use than OpenGL.
OpenGL has a learning curve, for sure, but once you get it down it's really not so bad. OpenGL is like a giant state machine. Each function call changes the state of that machine.
OpenGL itself is even more like a specification than a library, since all it ultimately does is specify interaction between you and your graphics hardware.
You could always start with a 2D Graphics API like SFML (
http://www.sfml-dev.org/), which abstracts a lot of the nasty OpenGL away for you.
Honestly, a great OpenGL resource is
http://learnopengl.com/
There's no reason to spend a huge amount of money on an expensive book. Even in my college OpenGL courses, we found websites like that more helpful than a formal book in some cases.