Yes please, enough with the console vs PC discussions. This is not the place for it.
Yea, unfortunately an Apple Mac Mini leaves much to be desired in terms of upgrade-ability. And no, I wouldn't even bother trying the game out on that...the Iris integrated graphics is rather undesirable.
Can do these upgrades for a little under $1200:
CPU+MOBO+GPU: http://www.newegg.com/Product/ComboBundleDetails.aspx?ItemList=Combo.2157964
PSU: http://www.newegg.com/Product/Product.aspx?Item=N82E16817438048
RAM: http://www.newegg.com/Product/Product.aspx?Item=N82E16820231568
SSD: http://www.newegg.com/Product/Product.aspx?Item=N82E16820147373
Coming this holiday, there should be plenty of SSD sales. Seen the 500GB model go down to $140 and even the 1TB model go down to $280. Don't need 1TB honestly. Can always still use a 1TB HDD for your storage files and just run applications on the SSD. I'm still rocking a 256GB SSD with two 1TB drives for storage because I don't have that many applications installed on my SSD at a time.
Another option for under $950 that would still get you Ultra settings:
CPU+MOBO+GPU+RAM: http://www.newegg.com/Product/ComboBundleDetails.aspx?ItemList=Combo.2471136
RAM extra: http://www.newegg.com/Product/Product.aspx?Item=N82E16820104458&ignorebbr=1
PSU: http://www.newegg.com/Product/Product.aspx?Item=N82E16817438048
SSD: http://www.newegg.com/Product/Product.aspx?Item=N82E16820147373
I hope you do have a decent case