<p>I want to continuously sample from my PC's audio line in using C# (then process that data). What is the best way to do the sampling?</p>

There are no built-in libraries in the .NET framework for dealing with sound, but if you're on Win32, you can use an unmanaged library like DirectSound to do it.
Ianier Munoz shows
how to write a full-duplex audio player in C# using
waveIn
via P/Invoke
on CodeProject.  He mentions
Managed DirectSound
as a more general method.