Do you need a DAC? Absolutely. Indeed, you can't do without one if the source media is digital. So it depends on the quality of DAC you want to stretch to, using either the DAC in the Mac Mini, the amp or a dedicated DAC unit. The dedicated unit clearly provides an opportunity to upgrade as funds allow.
In my experience, the biggest factor influencing SQ will be the quality of the source media, with heavily compressed lossy files sounding worse relative to lossless files. Ignore statements regarding uncompressed files sounding best. Lossless files contain all the information of the original uncompressed file, so you might as well save the space.