A while back I did A Modern OpenGL Resource Roundup, including links to the various GL libraries. There are also a ton of links that might help with your knowledge of OpenGL in general. I would recommend starting there.

I assume you are looking for a cross platform library to handle the stuff OpenGL doesnt ( Windowing, IO ). In that case, GLFW and freeGLUT are probably the most commonly used, although SDL or SFML can be used.

GLUT is just a utility library for OpenGL. You can do OpenGL without Glut at all (forget on Linux, but on Window's you just make a normal Win32 Window and put an OpenGL context in it using a few Microsoft wgl_ functions). A GLUT like library is Freeglut, another alternative is SDL and there are many more.

Ever heard of GLX + XLib? Works without glut. Glut isn't Linux domain either, and there is like a ton of way doing it:

Standard XLib + GLX (all in all each implementation running on X does this in the end)

GTK+ with GDK and OpenGL

Qt and QtGL

and tons of others...

Is it more performant than using glut?

The problem with GLUT is not strictly performance related, it is design related.

GLUT takes full control of your game loop and while that is fine for simple examples where the focus is on demonstrating or teaching OpenGL concepts its just not that suitable for games.

freeGLUT and QT have the same problem (QT is great for GUI applications though), you can hack around the gameloop stealing in both QT and freeGLUT but unless you really want other features provided by those libraries it is not worth the effort.

SDL, GLFW and SFML are all solid cross-platform options to use with OpenGL. (I'd recommend against using Win32 or X11 directly since those APIs are pretty darn painful to use and X11 might be replaced by Wayland or Mir on Linux in the near future anyway)

As for D3D vs OpenGL performance: it depends.

For old versions of the APIs(OpenGL 1.x, D3D<=8) it really doesn't matter, use something more modern, neither is suitable for modern hardware.

For semi-old versions of the APIs (OpenGL 2.x and D3D9) You have less API overhead with OpenGL (and thus you can possibly get slightly better performance with it unless your GPU manufacturer has bad OpenGL drivers (Intel GPUs will most likely perform better with D3D9 than with OpenGL 2.x)

For modern versions of the APIs (OpenGL 3.x/4.x and D3D10/11) the difference is pretty much all in the drivers, nvidias drivers are of equivalent quality for both APIs, Intels are quite a bit better for D3D, not sure how AMD stand today.

Personally i wouldn't worry too much about performance at this point though, the skills transfer between the APIs and by the time you're at a stage where every last microsecond counts the APIs and possibly also the market will be different from what they are today.

Also: Direct3D only works on Microsofts platforms, everyone else either uses OpenGL(Mac,Linux,Solaris,BSD), OpenGL:ES(Android,iOS) or some proprietary hardware specific API(Sony and Nintendo consoles), to hit all major platforms you will be forced to use several different APIs anyway.