As Tesserax mentions, the "Distribute a Range of IP Addresses" setting is very rarely used these days, since it normally requires that your Internet Service Provider (ISP) has provided you with a fixed bank or series of Static IP addresses for your Internet connections.
If the WAN port on the AirPort Extreme is receiving a Public IP address, then you would want to use the DHCP and NAT setting for Router Mode on the device. DHCP and NAT is also known as Share a Public IP Address, depending on the version of AirPort Utility that you are using to administer the AirPort router.
When you do this....and assuming that you have not changed the DHCP Range settings for the AirPort Extreme......the AirPort Extreme will have a LAN IP Address of 10.0.1.1, and it will pass out IP addresses to other devices on your network using a range of 10.0.1.2 to 10.0.1.200.
So, all of the network devices that are connected to the AirPort Extreme will receive Private IP addresses. In other words, NAT is acting like a simple firewall to shield your network from the Internet while allowing your Public IP to be "shared" with local devices so they can connect to the Internet.
That's why we asked what make and model of modem that you are using......so that we can recommend the correct setup for the AirPort Extreme based on the modem's capabilities.
It sounds like you are using a PC to administer the AirPort Extreme, correct? That might be a problem if you have the current "tower" version of the AirPort Extreme, since the setup is not officially supported with a PC. Some settings make "take" or "stick" while others do not.
If you can answer the questions that we asked above, we should be able to provide some help for you.