A NAS is not the way to go, unless you already have one (IMO).
A NUC with an i3 processor will do what you want (smallish library, not DSP intensive). You could get the last generation Nuc7i3 processor, 8 Gb RAM and the M2 SSD for about $400. Plug in a cheap USB drive for the music you own now and you’re done (assuming you can borrow keyboard, mouse, and monitor for the ROCK install).
Is this outside your price range?
You could buy something used. There is a Nuc5i3 for sale on this forum for $175
The most important thing is getting something with a SSD for ROCK’s OS and the database. The CPU speed isn’t that critical if you are mostly going to stream, but it should be an Intel processor.
BTW, I don’t believe a NAS will run ROCK. It would run RoonServer with Linux AFAIK.