I was told I could use my Apple Airport Extreme as a repeater only if the main router is another Apple Airport device. My Apple Airport Extreme is my main router. Any other options before I buy a repeater?

An Apple AirPort Base Station can only "wirelessly extend" a wireless network created by another Apple AirPort Base Station.

You can add any Apple Airport Base Station as a wireless access point to any wired network regardless of the router used to create it, by connecting it to that network with an Ethernet cable.