Which WiFi extender is recommended withAirPort Extreme 892.11m WiFi?

Which Wi Fi extender should I purchase?

Another AirPort Extreme 802.11n. You can find them on Ebay.

It is extremely unlikely that any other product from any other manufacturer would be compatible with your AirPort Extreme since Apple engineers designed Apple's "extend" option as a proprietary feature that would only work with other Apple routers.

If you don't want to go with another Apple product, keep in mind that your 802.11n AirPort is at least 7 years old, and as much as 10+ depending on when the product was placed into service. Average useful life of a router designed for home use is about 5-6 years, so the AirPort is definitely at the "long in the tooth" stage.

It might make sense to retire the AirPort Extreme and look at one of the newer mesh wireless systems to upgrade your WiFi performance. Apple is now offering the highly rated Netgear Orbi system, if you prefer to buy from Apple. Looks Apple is also selling the Eero mesh system as well as Linksys products.

The OP was asking about extending his network, not audio features. Please start another discussion if you are asking about audio questions.

Look at the AirPort Express. It has both analog and optical audio out. Unfortunately, the Express is nowhere near the WiFi performer that an AirPort Extreme is.

https://support.apple.com/kb/sp651?locale=en_US

But they don't have optical sound out - even Airport Extreme lacks this feature, no?