How to upgrade hard drive in Mac Mini
I recently did this very thing. I backed up my OS and files to an external drive (not a thumb drive), installed the new drive with new OS, and restored the Time Machine backup to the new drive. The whole process took a couple of hours. The best online video for doing this operation IMO is here: http://eshop.macsales.com/installvideos/mac_mini2011_hd/
Replacing the hard drive will not void your AppleCare warranty. OWC addresses this issue on their blog: http://blog.macsales.com/18244-owc-diys-wont-void-your-macs-warranty


NOTE: I have done the restore process in #1 using both Time Machine and Carbon Copy Cloner. Each is different, but relatively simple.