If you have Visual Studio 2013 Express for Windows Desktop (or VS 2013 Pro or better), then you have the Windows 8.1 SDK and will use it for any C++ project by default. To support 'down-level' systems such as Windows 8.0, Windows 7 and/or Windows Vista, you need to set the _WIN32_WINNT preprocessor symbol appropriately (_WIN32_WINNT=0x0601 for Windows 7 or later). There's nothing else special you need to do, and you can use DirectX 11.0, DirectXMath, XInput 9.1.0, etc. on all these platforms without any need to use the legacy DirectX SDK. The HLSL compiler (D3DCompile #47) DLL is available in the Windows 8.x SDK to just copy into your apps folder for Win32 desktop apps, although on Windows 8.1 it is already part of the OS as well.
Where is the DirectX SDK (2013 Edition)?
Where is the DirectX SDK?
Ideally you would avoid using D3DX11 and use any of the many alternatives available that support Win32 desktop apps on Windows Vista or later.
You can of course still also use the legacy DirectX SDK with the Windows 8.x SDK (which unfortunately you have to for XAudio 2.7 on Windows Vista/Windows 7; XAudio 2.8 is part of Windows 8.x), but you need to remember that the include/lib path order is reversed since the headers in the DirectX SDK are now older than those in the Windows 8.x SDK. This is covered on MSDN. Remember that if you use the legacy DirectX SDK components like D3DX, XAudio 2.7, XInput 1.3, XACT, D3DCompiler #43, etc. then you also need to rely on the legacy DirectSetup deployment. In this case, it is recommended you make use of the refreshed version of the REDIST rather than the one that shipped in the legacy DirectX SDK.
BTW, if you are trying to target Windows XP with the "v120_xp" Platform Toolset, you are actually using the Windows 7.1 SDK and not the Windows 8.x SDK since the Windows 8.x SDK does not support Windows XP. See this post for the many caveats of this scenario, or save your sanity and just let Windows XP go away :)