Is the only purpose going to be playing videos from the NAS? If so, it might be simpler to run plex on the NAS (or Jellyfin, that's the open source plex competitor, but I haven't used it so I don't know how good it is), as long as the NAS has a good enough CPU. Then you could just stream to a chromecast.
If that's not an option, then a NUC is probably your best choice.
Is the only purpose going to be playing videos from the NAS? If so, it might be simpler to run plex on the NAS (or Jellyfin, that's the open source plex competitor, but I haven't used it so I don't know how good it is), as long as the NAS has a good enough CPU. Then you could just stream to a chromecast.
If that's not an option, then a NUC is probably your best choice.