What are the right settings for the AirPort Extreme?

It would help if you can provide the type of Internet service you are getting (cable, satellite, PPPoE, etc.) and the make & model of the Internet router that your ISP has provided you to gain Internet access to their services. Based on those it would be easier to answer your questions.

1. Which of the following should I select in "Connect Using" under the "Internet" tab and why?

- DHCP

- Static

- PPoE

This would depend on the type of Internet service you are getting. For example, if your ISP is providing you with a dynamic Public IP address (typical for consumer-grade Internet service), you would set this to DHCP (the default). On the other hand, if they are providing you with a single static public IP address (typical for business-grade service), then Static would be the correct choice. You would only use the last option if your Internet service is via PPPoE.

2. Which of the following should I select in "Router Mode" under the "Network" tab and why?

- DHCP and NAT

- DHCP only

- Off (Bridge Mode)

If your modem is purely just a modem and not a combination modem/router or gateway device, then you will want this option set to DHCP and NAT.

3. On the Mac in System Preferences > Network > Advanced under the "TCP/IP" tab, which is the best setting for IPv6 addresses and why?

- Automatically

- Manually

- Link-local only

This will depend on, whether or not, your ISP is providing you with IPv6 service for Internet connectivity. If they are not, then "Link-local only" would be the best choice as it would limit IPv6 traffic to your local network. Automatically or manually would be used if you are getting IPv6 services from your ISP.

I have the Airport Extreme connected through ethernet to the aforementioned modem which is a modem+router but I have disabled Wi-Fi on it and I use the Airport as a router instead. Does that mean I should set the Router Mode to "off (bridged)" or "DHCP and NAT"? I'm confused because I don't know if the fact that the modem is also a router makes a difference, even if I'm not using it as a router.

FYI ... just disabling Wi-Fi does not disable the (modem+router) gateway performing as a router. As such, you need to reconfigure the Extreme as a bridge: Off (Bridge Mode) to function properly along with this gateway device.

I think my ISP provides IPv6 support, but I have not enabled it on the modem. "Automatic" was the default setting I found on my Mac in Network Settings. Should I leave it like that?

I would go ahead and reconfigure both the base station and any of your Macs for "Link-local only." You will only need to change it if your ISP does enable IPv6 services and you want to use them.