a NAS is indeed the best solution to achieve what you want to do i.e. centralizing all your movies in one place to be streamed across your home.
then you have 2 different possibilities to play it :
1. using your TVs and not buying anything else : if it's a smart TV with a DLNA client, you will have to find a NAS powerfull enough to use Plex as DLNA/upnp streamer that will be installed in your NAS. DLNA is limited in terms of file compatibility. Plex makes it possible to stream many file format to any DLNA products (smart TV, Playstation, xbox, BR player, tablets,...)
2. use a dedicated media player (WDTV Live being one of them), model will depend on what type of files you want to watch (SD/HD, audio HD, 2D/3D, ...). you will have to buy one player per TV. It's more expensive but results can be better than using plex (or the syno app) on your NAS.