However, what should i set the ISR to? I think FALLING would be the best, since it's pulled down?
Yes. And remove all Serial stuff from all interrupt routines.
Also i found out that the digitalpintointerrupt() is not recommended on the Due, since all DPins are able to interrupt.
You should tell us if you use another type of Arduino than the UNO. Without any mention of a special type we expect you to use an UNO.