Advice on best upgrade path for a Mac Mini setup

Internal or external are the same in regards to noise in your audio room. You don't want any spinning disk in the same room you listen to music in. Buy either a NAS drive or mount the drive on another computer in another part of your home.
1 thing I should have mentioned is that I designed and implemented a switched Gb network that all routers and devices attach to. Very fast for both audio and video.
as far as the GUI goes, the Lumin and DS Lightning software is light years ahead of the Mac based audio programs. I was using the 1st release of audirvana on the iPad and it was crude but I knew it is a work in progress. I like the DS software better but Lumin sounds better. What's nice I can pick which 1 to use.
With audirvana, I got rid of iTunes and let audirvana control everything which sounded better.

rbstehno is correct, ideally you want your NAS drive or music server elsewhere, my NAS drive is in my office and I listen in my listening room. And that's interesting info on the Lumin app I may have to check that out. One thing about the Lightning DS app for me at least I thought it sounded better on Ipad then Iphone.  I didn't have an Ipad when I got the Aries originally but I was able to pick up an Ipad Mini for around $200 very cost effective and I just use it as a remote control.

Thanks for your thoughts everybody.

Other than replacing the Mac with some dedicated streamer, what in your opinion would be the best value upgrade if I want to keep using it?
:-)

I have a Mac Mini with iTunes and Audiovana. How do you get rid of iTunes and just use the Audivana. Do I just buy the app from the iTunes Store. Thanks for any info or help. I'm using an iPad 2 to play music from its itune app.

Wow look away for a day and now I feel obligated to reply to  many posts in this thread! 

First, thanks to @rbstehno for a couple of well informed great posts.

Let me say that from my firsthand experience is based on using MacMini, Audirvana+, (as well as Amarra & Pure Music) Apple Remote for years. I had shootouts in my system with Aurelic Aries (not Aries Mini) including its linear power supply, other servers. I upgraded to Sonore microRendu & a linear power supply as streamer/renderer with my files stored on a Synology NAS in the next room. I run ethernet CAT6A cable to the Sonore(although you don't have to). I use Lumin app on iPad (or Android phone) for controlling the music. The improvement is TREMENDOUS!

IMHO, the advice to run a headless MacMini with internal or external harddrives, use iTunes (or Audirvana+) & Apple remote is good advice FIVE YEARS AGO, but not any longer. Sorry, but the disadvantages mentioned in a few posts are significant. Get the full purpose computer running a big mac O/S or Windows O/S out. Get the big noisy switching psu for the bigger computer out. Get any spinning discs out. Get optical isolation in. Use a single purpose computing solution( e.g microRendu, Aurelic, Aurender,  all running O/S with fewer processes. The mR also has optimized audio board with improved USB output which helps keep noise from getting to your DAC. This stuff is discussed in gory detail daily on a computer audiophile related forum that you should all read before recommending ten year old computing solutions. This stuff has changed too fast! 

Audirvana+ whether running atop iTunes or in its own mode(which sounds better, but introduces many painful database management issues) is not as user friendly as Lumin, Linn Kazoo or Aurelic's DS Lightning app. Library files get corrupted for many users and the fixes are painful; I've been there. 

The Aries Mini is a good product but needs a better power supply to perform at a high level. It's built in DAC is inferior to most audiophile DACS, but good for a starter system on a tight budget. The Aries at $1600 including a good LPS sounds excellent and is closer to the microRendu in sound quality IMHE. The Aurenders also sound good if you don't mind their cost.

As I posted last week, the  microRendu is incredible and only $650 + choice of power supple; it can stream Tidal, but you will want a NAS to store your own library. You won't need the mac at all unless you choose to use it for running HQ Player or similar to do DSD upsampling and/or EQ. Read the online reviews, especially Connaker's. It's a real Swiss Army knife! Cheers,
Spencer