Connecting a NAS to Airport Extreme and using the DHCP ISP connection

I just got a NAS system today from Synology, the DS412+ and am trying to configure it to work. Current setup: The NAS is connected via ethernet to the airport extreme and all computers, iOS devices in the house are wireless. The airport extreme settings are DHCP connection from the ISP and the router mode is off(bridge mode). This setup works great as long as everything is wireless but the problem comes when I connect my computer to the LAN port on the airport extreme. I am trying to copy my files from my old firewire800 hard drive and transfer the data over ethernet instead of wirelessly so that the transfer will happen faster. I am able to see the NAS and the airport extreme but I am unable to connect to the internet. Which leads me to believe that the NAS is also unable to access the internet which was one of the reasons I got it so that I can access it from anywhere.

When I change the router settings to DHCP from bridge mode I get the error below.

"Sharing a range of IP addresses using DHCP Only requires manually configuring your WAN IP address. If your ISP gives you a range of static IP addresses, you should manually configure your base station with the first IP address and distribute the rest via DHCP."

If I change the rougher settings to DHCP and NAT from bridge mode I get "double NAT" error and the internet still does not work.

I am looking at wiring up my house so that I can have a better connection to the NAS as well as the internet so this problem is not just a temporary problem.

airport extreme - 5th generation - firmware - 7.6.4

Thanks for the help.