Setting a router to be an access point

Verizon is awesome!

I haven't used any of Verizon's routers, but in general, most wireless routers and access points are supplied with fairly decent wizards to guide you through the setup process of your wireless network these days.

Whether you follow a wizard or decide to go for the manual approach, you should ensure that your wireless router broadcasts at least one appropriate 802.11 standard that your Xbox 360 and computer can receive. In general, 802.11b (4.5 Mbit/s) is your best bet for getting everything to work, although 802.11g is considerably faster (19 Mbit/s) and remains fairly well-supported, especially by wi-fi equipment created in the past three years. 802.11a is an obsolete standard, and 802.11n is an unofficial standard, so steer clear of them until you know the specifications of your receivers (clients).

You should also be sure to encrypt your traffic for this particular reason. WPA and WPA2 have been virtually impossible to crack until recently, whereas WEP can easily be cracked in 10 minutes by readily available software. You're not likely to run into anyone with the resources needed to crack WPA/WPA2 (e.g. the storm botnet), so unless you want to spend time setting up VPN tunneling via SSH, WPA/WPA2 should be good enough for now.

In general though, if you manage to refrain from doing obviously stupid (?!) things, such as turning off broadcasting, not password protecting admin login to your router, and submersing your router into an aquarium teeming with technophage piranhas, you will most likely do perfectly fine!