Next steps after connecting the beagle board

I want to try and compile to linux kernel sources.
I have a windows PC.
What is the best option to use to compiel the unix source ?
cygwin ?other tools ?

Also, I see the sources can be accessed via a git tree, how do I just
get all the sources from git on a Windows machine ?My git on windows
is just not working out well.

If I do buy another machine to have it dedicated to linux, which linux
OS is most advised ?I am trying to make progress quickly with a
windows machine though
Thank you
(I guess there are 3 questions here)