Nant is certainly worth taking a closer look at because it can save you from the mundane tasks of build and testing.
Ant is definitely worth considering if you mainly work in C#. Of course, you could use Ant to call Nant subbuilds! I must say that sounds like a recipe for headaches.
Often, the best way to learn is to download the bits and start to play. Try extending the build to extract source code from Visual Source Safeyou could even write your own extended Nant task!
Looking at my sample, I think I need an ASP.NET client; that should keep me busy until the next time we meet.