Those are huge files for rips, you should look at downsizing them to rips where the bit rate is about 10,000Mbps anything more then that and you won't notice the difference. Are these rips from movies you own? Do you care if you lose the files?
You can certainly go with the USB drive solution, however unless you have these rips backed up, you will lose whatever is on each USB drive when it dies. Also, depending on what media streaming device you are using, you'll only have access to what is on each drive when it is attached to a computer or streaming device via USB.
A NAS, while expensive, offers several advantages, firstly you get redundant storage, this is not to be confused as a 'backup' but simply storage with protection from at least one drive failure. A four bay Synology NAS with 4x4TB drives would give you just over 10TB of useable space when configured in RAID 5, you can plug it into a network and access the files over the network. This is what I do for the movies and tv shows in my collection, I have several NAS's actually of varying sizes and capacities. A NAS can also double as a network backup for other data, a time machine backup repository and the list goes on. As you have found out, a NAS solution is not cheap, but the advantages it offers make the investment worthwhile IMO and protect your data to a degree.