When you say you want fresh slate, do you mean files or configurations as well? If you don't care about either ones, just get the new hard drive, install the new OS on it, and you are good to go. If I were you I'd just purchase an external hard drive enclosure, and put the old drive in there. After you finished with the new install on the new drive, you can take your sweet time and copy the old files over as you see fit, when you are finally done, format the old hard drive and use as an external drive for data or time machine. The hardest process is actually opening up the mac mini and putting in the new stuff without breaking anything. The rest is simple.
Correct. I want it like it was basically a brand new computer with nothing on it except of course what comes standard. Is that what you are meaning by files and configurations?