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A really cheap and simple solution would be to pick up a used Airport Express to catch the stream from your Mac Mini and combine it with an inexpensive chip amp like this one.
I don't know about the current generation of Airport Express base stations but all the previous ones had both analog and digital output so you could go analog directly into the amp using a stereo mini to RCA cable or, if you wanted to fancy it up a bit, you could insert a DAC with optical input and use a mini Toslink to Toslink cable.
I have a setup like that in my garage workshop and it sounds just fine for that application. There's an ancient 802.11g Airport Express streaming music from the iMac in my office, then an AudioEngine D1 DAC I bought used for $100, a DIY Tripath chip amp and a pair of Boston Acoustic garage sale speakers. Total cost including the DAC was less than $200.