So I was planning to connect an external power supply to an Arduino to the Vin pin, Is 12 volts with a 500mA or 750ma fuse enough to have the board functioning properly. Also, how much current would left for the peripherals? By the way this is through a shield being implemented.
atmega328p allow pro pin source maximum 20mA, whole chip maximum 200mA.
the chip itself consumes 1.5mA.
UPD. Ah, yes, onboard 5V LDO regulator is able to provide ~100mA maximum.
You don't need fuse to power arduino through vin pin. You can even use 100A power supply as long as voltage is between 7 and 12V. Lower is better. Everything above 7V is just waisted as heat in voltage regulator.
How much current you can draw from the 5V pin with a 12V input has been highly debated on the forum.
For the total Vin current my vote is for about 120mA, that leaves about 60mA for everything else