DHCP on the modem and not router, why?
Because DHCP makes a device like the DIR a router. Making the DIR an AP means turning off the router feature and let the modem handle the router features. The DIR just passes on the connected clients through wireless (and wired ofcourse), hence keeping all clients in the same subnet. When you enable the DHCP feature, you're turning it in a router again and you will need to create a different subnet since two DHCP servers on the same subnet will reek havoc on your LAN.