To add to what rocksuitcase said, if you already have storage drives, a Synology NAS would be an excellent choice. A quick Amazon search shows a 4 bay Synology box (without drives) for $600. You could then put your existing drive(s) in it and add drives over time as you need them.
You could then get an Intel NUC, RAM, and SSD for about $250, and have that hooked up to your stereo (and monitor, keyboard, and mouse). The one I'm looking at right now (Intel NUC NUC5CPYH) is more than capable for what you'd want to do with it. Hook that up via USB to your DAC and you're in business.
A note about overclocking: generally when you overclock a CPU you'll need more cooling than the stock fan. This can be water cooling, or an aftermarket fan. I don't have any experience with water cooling but the radiators need fans, so it's not a completely fanless option. That said, some aftermarket fans can actually be quieter than stock fans while still providing better cooling. To be honest, though, I don't think overclocking is the way to go for you in the situation you described.
Ultimately there are so many variables at play here that it's hard to say definitively what is the one right answer for you (assuming there even is only one right answer). I've experimented with a lot of different arrangements, and I'll tell you what I've settled on and am happy with.
In a spare bedroom I have my main PC that houses all my data, and that I use for things like audio editing and torrenting. It's just running Windows 7, and I share the folders that have my music. I have it connected via ethernet cable to the router. Then I have a Raspberry Pi in the basement that serves as my headphone listening station, running Volumio. That is also connected via ethernet cable to the router. In the living room, connected to my stereo, I have a small PC (again connected via ethernet cable to the router). This PC runs Windows 10, and I use foobar2000 for audio playback. If I wanted to, I could use this PC for word processing. I do use it for streaming video (HBO Go, YouTube). It's also capable enough to do audio editing. Here are the specs: Intel Pentium G3258 CPU, 8 GB RAM, SSD, ASRock H97M-ITX/AC motherboard, Mini-Box M350 case, wall wart power supply. The main reason I have a PC hooked up to the stereo is because it's easier for my ol lady to use. If it were just me, I'd have a Raspberry Pi hooked up to the stereo rather than an actual PC. A Raspberry Pi is more than sufficient for audio playback, and I'd just use my PS4 for all my video streaming.
Anyway, I hope this hasn't just muddied the waters more for you. If you can narrow down your specifics even more it will be possible to make more pointed recommendations about what may be good for your situation.