P.S. If you do go in the market for a wireless printer I have the previous model (HP 6980) of this one:
HP 6988 It is Great. Although it does work wireless, I have it directly connected to my router via and Ethernet cable. All my computers can access it through the router/LAN.
If you ran it wireless, in theory you could set in on the back porch and print to it.
It can also connect direct to a computer as a USB connection if you want it dedicated to a single computer, (or shared through one computer like you're trying to do).
I almost gave up on HP since my last printer was a P.O.S. When I was looking again the reviews of this one made me try HP again, I'm very satisfied. Prints fast, ink cartridges last, no problems or jams. Bought a two-sided attachment use dof on ebay for duplex printing capability.
(Replacement cartridges ar $25 a pop though....) Have to budget for the 3 pack at COSTCO...