You need a small PC, a NAS box and the drives to load into it. A new NUC mini PC goes for about $350 by the time you get an SS drive and memory installed. That is for an fairly high performance i5 processor. A lessor processor will cost about $100 less.
A 4 bay NAS is another $300-$350. Drive price depends on size. I have two 4TB drives in my NAS right now (I can add 2 additional drives in the future). They run in a mirrored configuration and provide 4TB of storage. That's my whole collection, surround and stereo, and the drives are barely 2/3 full. The drives go for about $150 each.
The media player software is free for Kodi or Foobar, and under $50 if you need to run JRiver. That totals up to about $1000 complete for the media player.
And of course if you already have hardware that functions well for you as a streamer, you can skip buying a separate computer to use as a playback device.
While I understand the appeal of multi-bay NASes and have lusted after them in the past, I think it's less expensive and arguably more secure to buy multiple single-bay devices and back one up to the other. RAID is definitely useful and convenient, but it's not technically backup. If all your drives are in one box and something goes catastrophically wrong with that box and damages all the drives, you're in trouble. On the other hand, if you have multiple NASes (or other drives), the complete failure of one won't affect the other.
I actually ran a hybrid setup for several years: I had a pair of two-bay NASes that each had two RAID 1 mirrored 2TB drives. But rather than just trusting RAID, they were each backed up to other, cheaper single-drive boxes. The backup drives can even be in a separate room (or if you're really fancy and have a good network, a different house).
As a general rule, the more you know about Linux, the cheaper you can do this stuff as well. A very inexpensive computer with cheap attached USB drives can act as a NAS with far more flexibility than a mainstream consumer NAS usually offers. The downside is that it may require a level of skill and amount of learning that far exceed one's interest.
It's also technically possible to do that with a Windows computer, but I had bad luck with both Vista and Windows 7 randomly deciding not to serve data any more. It's possible that's less a Windows shortcoming than the techno-curse/little black cloud that follows me around to punish me for being a bad person.