Plex was originally a fork of xbmc. They do not look that similar though. Plex is lighter and has a server client model. XBMC is heavy, better looking and is a single application.
I run 2 NUCs both with XBMC and a server. All on ubuntu, but no reason not to use windows other than cost for no gain. If you only want XBMC on the NUC then checkout openelec.
Would there be any benefit, other than cost, using ubuntu on the NUC and the NAS? Would it matter that my desktop is Win7 (for steam, MS office)
Does openelec have a web browser? I would want the NUC to have browsing capabilities.