Making an engine cross-platform means forcing yourself not to use system shortcuts. This means higher quality code on most cases and shouldn't affect performance, unless you're doing something on a really low level, what probably is not your case.

But consider that making an engine cross-platform between Windows Mac and Linux will automatically make it easier to port it to game specific platforms and consoles, since the independent code will already be independent.

My father told me once that unplanned work means doubled work...

If this is an engine that you intent to use in order to actually make games and maybe release them, you may be losing profit here.

But if it is just a "learning experience", you have no real reason to worry, include that win32 with all your might!

Have you made a complete game before this game engine making adventure?

the only benefit I really see using directx is support for the Xbox which would obviously not be an option for a platform. Both apis have all needed features for creating modern games. I just prefer OpenGL over directx just because of its wider support over multiple platforms.

Neither really hold a strict advantage over the other. In terms of platform support there's a good deal of market-share/revenue-potential overlap, but also exclusive support for certain platforms in either camp -- For example, if you want to run your game on XBox One, Windows RT (Surface, et all), or Windows Phone, you need to support Direct3D; likewise, basically every other platform runs OpenGL or OpenGL ES -- Although "more platforms" is a decent enough argument in favor of OpenGL, in practice the D3D ecosystem is probably about equal to the GL-based ecosystem in terms of dollars (if not users) available, but the GL-based ecosystem is more fragmented (linux, MacOS, iOS, Android for starters, and myriad hardware devices to finish) so its more work to tap all its potential. In the D3D-centric ecosystem, you can reasonably ask for more money for your game, whereas the bulk of the GL-based ecosystem is iOS/Android, where you reasonably can't and have to design around and subsist yourself on micro transactions for the most part. Anyways, none of this money stuff might be a concern for you now, but its worth bearing in mind for the future.

Other than that, Direct3D is a little more "modern" in its features and syntax (for better and for worse), but the two are close enough in functionality that you can create an abstraction layer between the two without much trouble. Pick one and learn it using contemporary best-practices, and all will be fine.

Some benefits of each, excluding API preferences:

- on Direct3D shaders may execute a bit faster, and drivers are better tested, so you're less likely to get into customer support hell for your game

- on OpenGL you will get a bit faster drawcalls (less CPU overhead per drawcall)

For the "shaders execute faster" point, see http://aras-p.info/blog/2007/09/23/is-opengl-really-faster-than-d3d9/ which is fairly old, but that still seems to hold true for today's hardware, at least on quite basic shaders (blinn-phong lighting, shadowmapping)