Almost all new laptops comes with wireless device built-in to their system, only difference is whether they include a B/G type, G-only type or B/G/N type (these are mostly the reach of the wifi signals and whether your device can receive them - frequency/spectrum). G can receive both B and G, N type depends on the broadcaster on whether using a Draft-N or not. So, wireless-wise, you won't have issues, only leaving the password to access it (if it's free or subscription if it's paid-type). The cox cable will let you surf wired, for in the event the location you are at have a socket for it (and somewhat when at home, you don't have a wireless router - thus can connect directly to the cable or ADSL modem).
Power saving? yes, but only if you don't run many applications or intensive ones or setting your power usage to maximum performance or display to be the brightest settings, else it won't make any difference.