Why not - given the volume of files look at Plex on a NAS - this will give you the video side and you wont have to move the files with each computer change. Plex player is available for desktops, smart TVs Apple tv, IOS, AndroidI understand that streaming is a great way to go.
Some NAS manufacturers have itunes server software that might solve the music side for you too?
A futher side benefit is you can also run time machine servers from NAS devices too - possibly giving you another service that could be useful