Definitely get the official Xbox part. It plugs in cleanly, snaps to the casing of the Xbox like it was meant to, works perfectly, and hasn't presented the slightest problem for me. Setting up a third-party wireless bridge will work, but it's a pain to do, requires you get a laptop into the act, and even after it's working it will need to be rebooted occasionally. But if you get the Xbox part, you just plug it in, turn on the Xbox, and enter all the network settings right there with the game controller and then it Just Works after that.

You will get slightly better network performance if you run the 50 feet of ethernet cable. A few extra milliseconds of ping time in online Halo, slightly faster game downloads, etc. If that's important to you, run the wire. Otherwise: Xbox wireless adapter all the way.

I do want to point out how awesome the Playstation 3 is in this regard: Wifi is built-in, as is HDMI, I didn't need adapters for those things like I need for the Xbox.