Is this to use standalone or with Arduino IDE?
From quick look, the minimum you need is a 3.3V power supply, and either an RS232, USB or JTAG connector. A pullup on FWUP and probably access to the ERASE pin. I may have missed some things. For any real use you will also need to add the bypass capacitors to the power supply and other filtering. Aned the LED of course.
I think the simplest option is to use a TTL-Serial adaptor connected to the Debug UART and program via SAM-BA. If you want to program via Arduino IDE, I think you just need to add the "native" USB port. I don't think you need the ATMEGA16U2.
I have to wonder whether starting with a 144 LQFP SAM3X is the easiest way to get into building ARM boards. Something like SAM3S/3N would be simpler, although I like the NXP LPC1343 chips, they are really easy to use.