You definitely will need a static IP. DHCP servers will try to maintain an address for a device, but it's not guaranteed and should it ever change, your port forwarding will break.

The router might allow you to make a particular DHCP client static, but remember that if the router/modem is ever changed or if its configuration is wiped out, all of that will break. Usually best to configure static devices statically on the device, using IPs out of the normal DHCP pool range (ie. .10-50 is pretty safe).

You should need:

1) incoming ports to forward
2) IP address of the device to forward those ports to

"Private port" should be the same as the public port (or perhaps blank if allowed), otherwise you'll likely be configuring port forwarding, which means what comes in on 41790 is being moved to 80 on your internal network (which I doubt is what your device is looking for).

Finally, I should point out that the router portion of the SMC modem used by Rogers is crap.