Using two AirPort Express Base Stations (AX) should meet all of your networking needs. You would connect one, via an Ethernet cable, to your Internet modem. The other one would be configured as a wireless client for the purpose of sharing the printer that would be connected to the second AX's USB port.
Thanks, this is helpful. My new airport arrived in the mail and I am trying to set it up. However, I can't get my computer airport utility to detect the new airport (airport flashes orange). I tried disconnecting my original airport and connecting the new one to the ethernet just for configuration purposes but this didn't seem straight forward either. Do I need to have ethernet connected to both airports for it to work? I was hoping to use the other airport by just connecting to the first wireless network (which I think is what you are suggesting) and then to my printer to avoid dragging an ethernet cable through my living room.
Thank you so much!
By default, your new AirPort Express will broadcast an unsecured wireless network with a name like "Apple Network NNNNNN." WIth the original Express providing a wireless network, you just need to temporarily "switch" wireless networks to the one provided by the new Express. Once you do, you can open the AirPort Utility, select the new Express, and then, make the necessary changes. Allow the new Express to restart.
Once it has restarted, go ahead and "switch" back to the original wireless network. You should now only have a single wireless network to connect to. Your new Express is also connected to this network just like your computer is and it now should be available for printing.