OpenGL is much better these days and if it's your first foray into graphics programming learning WebGL is not a bad start IMO. You might need to use a browser that can support some of the OpenGL ES features (WebGL extensions) like VBO's and such but you can get really far that way.

Vulkan is not the right choice if you're just getting started unless you're already motivated and intensely curious (ie: already have some decent exposure to OpenGL, multi-threading, and are curious to know more).