How many computers do you have connected to your home network already?

You can get an "Access Point" basically all you do is hook the ethernet jack into your access point station and then into your wired ethernet router.

OR

You can buy a Wireless router. A wireless router has ethernet ports on the back as well as a wireless base station. You can basically throw away your old Linksys wired router and hook up everything to the new wireless router.

Also a word about 802.11b,g,n,etc . Depending on how fast your outbound internet connection is there is absolutely no point to go out and buy the latest and the greatest 802.11 draft N wireless router for some crazy amount of money.

For example, at my house my DSL caps out at a download speed of 2.5 mbps. We have an 802.11b wireless network that has a max speed of 11 mbps. If we were to upgrade to say an 802.11g network with a max speed output of 54 mbps the internet would not get any faster. However if you were transferring files between computers on your local LAN network then yes the speed would be faster.

Nowadays 802.11g wireless access points and routers are really cheap so it is worth it to just get the 802.11g wireless access point. I have owned a Linksys WRT54g access station for almost a couple of years and it has yet to fail me.

The trick is configuring. When you get it read the instructions on how to edit the configuration settings in the router. You should change the SSID (broadcast name) to something cool like, "Awesome Family" and enable WPA encryption with a password that something the whole family can remember. Also change the broadcast channel to something like 8 or 4. Just don't use the default.

I'm not sure how big your house is, but if it isn't huge (eg a mansion) then 1 wireless base station can cover the entire house.

For the Xbox the graphics of online play won't be affected by connection speed only the lag of the multiplayer games. Lag meaning you will see other people stutter when they move around. For Xbox live if you have DSL/cable then he won't have any issues playing.

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-Typos courtesy of my mobile phone.