Ivan, please recommend the minimum but capable dedicated PC setup. Since it would be dedicated, you can specify the software environment however you like ... wag lang command line. Of course bang-for-buck.
Might a customized dedicated netbook do?
For reliable DXD playback, I suggest going for a dual core desktop/notebook processor (not a netbook/nettop processor). It can be a cheap build using a Celeron or an Athlon x2 processor. 2 GB of RAM is sufficient for this purpose (4 GB would be a comfortable spec), and I suggest running Windows 7 or Vista for file compatibility (especially for the WMA format Studio Masters). Also, running the drives in AHCI mode help significantly.
The higher Brazos-based netbooks/nettops (E350/E450) can often handle 192/24 if you disable visualizations, desktop effects, etc. (and sometimes even your antivirus) and don't do much else. Atom-based devices are at a disadvantage for this use, but will often handle 96/24 smoothly as-is (as long as it's not a low frequency single core model).
The fastest Atoms are less than a third of the pace of a current entry level processor, like the G530. That means utilization will most likely be fairly high during playback, and that is something that you would like to prevent when playing these files. High sampling rates mean that you get through so many thousand samples worth of data in ever shortening spans of time, so packet latency becomes critical. Your computer has to transfer more data and has to deliver it with lesser delays. I'm not saying that it's not doable with a stripped-down computer, but it might be a hassle in the long run.
I would truly encourage you to test it, if you would like to pursue that option. You can start by turning off Aero, indexing, and all the other fluff in windows and maxing out your buffer size. If you have a dual core Atom at least and are running AHCI, then you may be able to hack it (depending on the downstream gear that you're using).
If you're willing to forego compatibility with some files, a Linux-based build might be able to play high res files with a lower spec computer (most name-brand music servers and streamers rely on a VIA-based computer inside). The main downside being driver support for Linux is generally bad.