Current macMinis will run ML - issues may occur when apple changes the hardware.
Since Mavericks has only just been released, most stock in-store probably hasn't been updated yet...

The easiest way to install is with a clean disk image.
You need another mac with ML to be able to create the disk image
Then install it on the MacMini using target mode via firewire.

there are no ML 'instal discs' for MacMinis because they don't have CD/DVD drives...

S