I am setting up a new network. Is NAT configured on the perimeter router, or the ASA5505 firewall?
Depends on the addressing you have been allocated. A typical setup is a service provider controlled router and they then allocate you a block of ip public ip addresses. One of these will be allocated to the inside interface of the SP router and the rest you use on your own devices.
Usually the device you place behind the SP router is a firewall so it is normally done on a firewall.
It depends, I usually prefer to do it on the firewall.