As I am starting to get Linux working, will it become possible for my Linux box to work with my Windows Network? Or will they not be able to talk at all?

If you install Samba, then it is quite possible to access Windows shares from your Linux box ("man smbclient", or "man smbmount" if your kernel has been compiled with smbfs support). Samba also allows you to configure shares on your Linux system that can be accessed by Windows just as well as ordinary Windows shares (in my experience, Samba actually performs better than real Windows).