I'd get a Synology NAS. It can hold your movies and do tons more, I love mine.
Thunderbolt on the mini is indeed probably overkill (and option limiting), plus even your HD content is probably not encoded to over 5 MB/s. It could be on a USB 2 thumb drive plugged into your router and look great.
Check the reviews on NASes on Smallnetbuilder.com & Cnet (Dong Ngo), Synology & QNAP always get top marks for great hardware, OS, expandability, etc. For example, I can stream stuff from my Synology via Airplay to my ATV without even re-encoding it, which is pretty slick. . brand new feature. DLNA, Plex, iTunes server, etc., etc all built in. And it does Time Machine for my macs and also backs up my windows 8 machine, and a million other things (hosts my printers for Airprint, downloads my torrents, mounts my ISOs via network, etc.)
I have mine connected via gigabit to a gigabit switch and can get pretty good transfer speeds (more than enough for streaming via wired or wireless) as well as backup and file copy, etc. What's also nice is last two OS upgrades to my Synology unit (annually or sometimes quicker) my transfer speeds have gone up noticeably.
I have a 212+ w/ dual WD Red 3tb drives in it, total cost maybe $600ish a year or more ago. I upgraded from a lower level Synology which was quite easy.
And if for some reason insane transfer speeds are what you want over a network, they make plenty of dual gigabit models w/ link aggregation (you need a switch that supports it as well), and you can even put a single SSD in along with multiple spinning drives to get some sick caching.