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. 

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. 

Reclocker will do nothing to improve asynchronous USB connection that he has.  Since async USB timing is not important then improving on this timing makes no sense.

Tgrisham, music doesn't "stream to DAC" in his asynchronous USB, but is downloaded as data in packets.  It doesn't make any difference if it comes from small or large buffer memory.  I might make a difference with synchronous USB or SPdif.