Hi
I wanted to do something similar to control my heating adjusting the start time automatically if its colder so in the winter it would come on earlier depending on the outside temperature. I even though it could learn how long it takes to get to temperature depending on how cold it was and adjust accordingly.
I looked at the WIFI shields and thought I may be beter using something like this http://www.ebay.co.uk/itm/Mini-Travel-Wireless-N-WLAN-Router-Access-Point-Adapter-/300556193704?pt=UK_Computing_Wireless_Routers&hash=item45fa8b8fa8&_uhb=1 an access point with an Ethernet shield that way all the WEP/WPA stuff is done externally and maybe I can pinch 6v from the PSU to power my arduino. Its cheaper too !!