I'd recommend exporting your project using the "Export File" option, and select "Best (ProRes)" for Quality and "Better Quality" for Compress. If you're going to be burning a standard-def DVD, for resolution 540p is the best option (if available; if not go with 480p). If it's going to be a Blu-Ray, then I recommend 1080p.
Of course, you could always get a nice USB external Blu-Ray burner for your Mac Mini for well under $100 (they make USB-C -compatible versions, too), and also purchase the Roxio Toast software if you want to burn polished-looking DVDs and Blu-Rays directly from your Mac.