The most limiting factor is the amount of RAM available, as it will have to be divided between the Host the the Guest OSs, if you want to have at least 3 OS running, and this depends a lot on each of these OSs requirements, you really shouldn't have less than 8 GB of RAM, however, the Mac Mini uses integrated graphics which doesn't have it's own memory and uses the RAM (1.5 GB). So, again, nothing less than 8 GB of total RAM.
Last edited: Jan 30, 2016