Hello,
I'ma Windows developer, and usually would recommend using DirectX and C++ to develop this tool, as audio/video processing, or, in this case, interception of an existing audio stream being transferred through(in or out) of a Windows system, will require low-level functions to make the audio capture happen in a "clean" and high-quality way.
Your budget though will not work for Me. I'm from the UK, and charge around £25 an hour, for this kind of work.
Cheers