My hardware is quite old now (positively ancient in computing terms), but it does everything I ask it to, with cpu cycles to spare. MySQL is pretty lightweight, and if you are prepared to configure things from a command line and not use a desktop, a minimal install of Ubuntu will be lightweight too. Given a fast HDD in the NUC, I don't think you would run into problems with it not being able to do what you want. Of course if you start serving 40~50Mbps bluray rips to multiple clients at once, you probably will get issues, but that'd be more down to network or disk bottlenecks than lack of cpu grunt.
I'd expect an i3 to be able to run Ubuntu minimal, MySQL, XBMC and serve a file to a remote client without breaking a sweat.
Having said that, a NAS would remove the need to serve files from the NUC, and you can tuck it away out of sight. It does up the cost though.
If you have some old hardware that you could repurpose, then you might be interested in
freenas.