Extend Signal with CenturyLink Modem/Router

Is it possible to use the any of the Airports to extend the C2100T wireless signal? I checked with CenturyLink, and they said that the C2100T works with third-party wireless extenders, but they could not advise on how to connect the Airport devices.

Sorry, but no. Apple uses a propriety scheme for extending via a wireless connection that is designed to only work with other Apple base stations.

One other option to create a roaming network is to use powerline adapters as pseudo Ethernet runs using your home's electrical circuit ... so, for example, you would get a pair of these. Place one near the C2100T and another where you want to place the Extreme to "extend" wireless network coverage. Each router, in turn, would connect to an adapter by Ethernet. Anyway, it may be worth considering to be able to use all of your base stations.

I notice that they are rated by speed, but how well do they function?

They have come a long way since they were first introduced. They are not as fast as a "pure" Ethernet connection, but their speeds have been improving over time. Currently home Ethernet is either 100 or 1000 Mbps to compare against. They also need to be on the same electrical circuit to function properly. I suggest checking with the store's return policy and getting a pair to try out.

My internet is currently 40mbps down, and the cheapest powerline adapter carries 200mpbs so that would seem to do the trick.

Remember your Internet "speed" will, most likely, be the slowest link in your overall network. Both local wireless or wired networks have much greater speed ratings. However, we do tend to perceive speed from an end-to-end standpoint. Think of it this way, improving either or both your ISP-provided Internet speed and/or your local network speed should result in a perceived (and measurable) increase in data transfer rates between the remote server and the local host.

As far as setup in the Airport Utility using the powerline method, would I still create a roaming network as you had previously described?

Yes, the poweline "Ethernet" circuit is just a substitute for actual Ethernet cable runs. Again, with powerline, you are using your home's electrical circuit just like an Ethernet cable run.

Unfortunately, the room where my modem must be placed is on it's own circuit in terms of outlets, and therefore it seems as though the powerline adapters would not work in this application. Is that correct?

Typically, yes, but unless you try you won't know for sure.

If so, my only options are to wire the Extreme as a roaming network or purchase new routers that work with the C2100T. Do I have to use the Extreme instead of the Express as a base station? Will either model cause more or less interference when placed in the same room as the C2100T?

Neither would make much of a difference as far as Wi-Fi interference is concerned. The Extreme does have the advantage of Gigabit Ethernet ports; whereas, the Express only employs 100 Mbps ones.

Finally, does the Extreme support AirPlay? I noticed that there is no audio output jack, and ideally I would like to connect each of these devices to a stereo.

Only in the sense that it is a wireless router, and like any other wireless router, it will support the AirPlay IP protocol suite ... but, as you noted, it does is not an AirPlay-enabled device with a built-in audio circuitry. For your goal, it would be better to use the Express instead of the Extreme.

Unfortunately, the room where my modem must be placed is on it's own circuit in terms of outlets, and therefore it seems as though the powerline adapters would not work in this application. Is that correct?

Powerline works best when the adapters are on the same electrical circuit, but powerline can also work OK if the signal must "hop" from one circuit to the other. As you might imagine, there will more signal loss as this occurs, but the results still might be acceptable.

The bottom line with powerline is that you won't know how well.......or, even if.....powerline will hop circuits in your home until you actually try it out in your home. For that reason, it would be a good idea to understand the store's return policy before you buy.