wxWidgets generally supports OpenGL rendering much better than DirectX and the library is simple but unfortunately it is messy as hell with years of cruft. It was also based on the design of MFC in the early days (when two stage construction was "a good idea") making it a bit horrid.
Since Qt requires an external parser to compile (it isnt 100% standard C++), people don't realize this yet but in ~10 years it is going to be as hard as Borland VCF C++ projects to compile.
So my suggestions...
There is a version of GLUT for DirectX called DXUT (in the DirectX SDK Samples). If you are confident enough to load your own textures / sounds / shaders etc... without SDL or other frameworks, then I highly recommend it. Since DXUT (and GLUT) is extremely small, it also keeps your software portable to other platforms at a later date (such as that crippled Windows 8 Metro stuff). If you don't want to write your own texture loading stuff then you can still use standalone libraries (FreeImage, DevIL/OpenIL, even SDL just for images).
Since you are using DirectX (with a GUI toolkit), you are probably only interested in the Windows platform. Since C++/CLI or C++/CX are "Microsoft standards" then perhaps you might want to try using Winforms to create the DX rendering context using those compilers? The rest of your code can remain 100% standard C++. If you don't mind constantly asking Microsoft (every 30 days) for a developer license, then you might want to use the Windows 8 Metro framework as a GUI / rendering context too.