After reading documentation I have concluded that developing an own "VSPackage" is the most powerful way of extending Visual Studio's behaviour.
Now I want to build an extension which modifies the build (compilation) behaviour of VS for C/C++ applications. Is there any getting-started guide or documentation on this?
Most available tutorials seem to focus on GUI aspects.
You want to modify the .vcxproj-file, it controls the build process for c++ in Visual Studio 2015.
You can read more about the build process for c++ in VS2015 here: Building C++ Projects in Visual Studio
If you're going to have several project that are going to use the same build process you should look into creating a project template instead of an extension. Take a look here to get started https://msdn.microsoft.com/en-us/library/xkh1wxd8.aspx
Good luck!