I would recommend getting a Linksys WRT54-GS wireless router (802.11g w/ speedboost). For the computer you need a USB Wireless "dongle" (Linksys and D-Link both make good USB Wireless dongles) if you have a desktop computer or a PCMCIA Wireless card or a USB Wireless dongle if you have a laptop. Most laptops don't have an abundance of USB ports so that's why I suggest a PCMCIA card. If you have a newer laptop (past few years) it should have wireless built in.
For the Xbox, Walmart sells a cheap USB Wireless dongle ($20 I think).
Here's a fast price breakdown.
Wireless:
Router - $50
USB Dongle $50 (max)
Xbox Dongle $50 (max)
Total cost = $150 (max)
Wired:
3 wall jacks = $30 ($10 each) conservative
500' Cat5e cable = $50
Network Switch (5 port) = $20
Punchdown tool = $10
Drill & Fishtape = Cost unknown/variable
Time spent fishing wires through walls = pain in the A$$
As you can see, wireless may be more expensive (I doubt it though if you looked for good deals), but you are free to move furniture around without having to string cables. If you hardwire network cable in and then decide to move your TV and Xbox, then you'll have to string new cable or move the jack.
The main concern with wireless is security, but like I said, there are simple tutorials out there that will guide you through setting up security. In fact the Linksys WRT54-GS is really simple to setup the security.