Virtually any wireless printer will work just fine as well as a printer that connects using Ethernet. If you are looking at an All-in-One type of device....all functions like print, scan, copy, maintenance, etc will be supported.
If you are looking at USB devices, Apple does not provide a list of compatible models, so It is difficult to say with certainly what will work and what will not. In general, most USB printers will work.
But....very important....if you are looking at an All-in-One USB device, you need to keep in mind that only the print function will work when the device is connected to the USB port on the AirPort Extreme. Scan, copy, fax, maintenance, etc. will not be supported.
Bottom line...if you are looking at an All-in-One device and you need all of the functions, you need to choose a device that connects using wireless only or Ethernet, not USB.
See this Apple document:
As far as USB printers, I don't know of any restrictions.
Question: Can I use a USB printer and hard drive at the same time
Answer: Yes. To learn more, see Uses for the USB port of Time Capsule, AirPort Extreme, AirPort Express.
As far as ethernet or networking printers, they do need to be on the Apple list.
Which are you using?