I had a couple of Memorex DVD burners that were USB 2 connected to my iMac. I burn a lot of discs. Had them for a little over two years and they started to give me trouble. I just dumped them and bought a couple of LG USB 2 drives, DVD CD burners from New Egg I think for 30 bucks. No reason they won't work just as well with a Mac Mini.
I have always been a little paranoid about those internal Mac drives. they are generally not state of the art in terms of burn speed and once, a long time ago, I had trouble getting a disc out and haven't really used the internal drive since.