Replacing a MAC Mini with new one...

Mesh, Since your asynchronous USB/Spdif converter is shielding your DAC from any noise or timing issues computer becomes irrelevant. Any MAC will do with any amount of memory, any hard disk and any playback program.  I'm in similar situation being shielded by WiFi connection.  I got new Mac Mini since my older Mini refused to load any OS higher than Snow Leopard.  The new one had Yosemite and currently I upgraded for free to El Capitan.  My Mini has 250GB SSD and 16GB of memory plus external 1TB HDD.  I got 16GB since in it is not up-gradable in new Minis while it is also my main home PC.  External HD can be of any type - I use Firewire with Thunderbolt/Firewire converter but only because I had Firewire before and I like it.  USB HD would be perfectly fine.  Get at least one more for the backup.  Don't trust RAID alone. 

Kijanki, Since I will use this Mini as a dedicated music server I am thinking I will purchase one with the 250 GB SSD, 8 GB memory, and what ever OS that comes standard. I forgot to mention that I also use Pure Music for playback.  Is it your thinking that the use of the USB converter negates concern over using an external USB HD for music storage and USB for playback?  

Another thought, will use of a USB converter negate concern with using an internal HD for music storage?

Thanks for your thoughts on this!

Mesch,
Recommend getting the max amount of memory. If you later decide to try a different software package such as HQ Player, you will be glad to have as much memory as possible. Also, as file sizes and your library grow, loading art etc. will be faster with more memory. 

Not to derail your original thought process but have you also considered alternatives to the MacMini approach including keeping your library on a NAS in another room and going with a low powered streamer/renderer to play the music on the NAS (and online if interested too)? There are many products to consider and my experience using MacMini for years is leading me down that path. Computeraudiophile site has the detailed threads on most of the pros/cons to this approach and specific recommendations.
Have fun either way you decide, Cheers,
Spencer 

Mesh, your USB/SPdif converter strips timing from the data.  In asynchronous USB data is delivered in packets at its own timing that has no connection with clock used by D/A converter.  Furthermore, Pure Power prevents jitter induced by noisy computer supply.  Pure Music is fine, since you already have it.  8GB is not necessary now (I run El Capitan on notebook with 4GB), but is probably a wise choice for the future.  Yes, you can use the same USB, since at this point only data (and not the music) is delivered to your converter (slight delays are not important).  Situation is different on SPdif side where timing is crucial.  I believe that your converter has both Toslink and coaxial outputs.  Normally coaxial should be better but try both if you can.  It is system thing and in some cases Toslink works better.  If you use coax, try to buy or build one, that is very short, less than 12". The shorter the better.  If you cannot do it then get 1.5-2m.  In first instance you won't have reflections in the cable (from the end of the cable) affecting transition while longer >1.5m cable will delay reflections making them miss original transition.  Try different digital cables.  It is characteristic impedance matching and more expensive cable is not necessarily better.

Get the least expensive slowest new MAC.  SSD is not required but it is quiet. Use power filter for your DAC if you cannot use different outlet (different phase) for computer. 

Sbank, I have and continue to consider other options. Would consider a basic server that could read AIFF files off a HD. 

Kijanki, thanks much for your input. I am using BCN connection between converter and DAC, direct connection w/o cable. I have 3 dedicated lines, one for digital.

In my household I have a Mac book pro which I use for general computer use and to serve music to my secondary systems, and the mini for my primary system.  What are thoughts in usng the MAC pro to burn CDs  and transfer file to HD and then using the HD with the Mini?