Martin has some good suggestions. For relatively low data transferring and wireless comm's with great range to the computer, I love Xbee. Much much better than Bluetooth which I've always found to be a bit of a pin tbh. However, if you want to get your board up and running on WiFi, whether you need the extra bandwidth, range, or internet connectivity, then I'd recommend the official WIFI Shield
. A while back I would have recommended the WiFly shield (notice the l in Fly, it can be confusing) which has a great library, and indeed I originally wrote the WiFi chapter of Arduino in Action with the WiFly, but then Arduino went and released an "official" WiFi shield. It's implementation is more consistant with the rest of the Ethernet library included as part of the main Arduino IDE and so I'd recommend it #1. If you go the WiFi route, the book includes instructions and a sketch using the official WiFi shield, but just in case you use the WiFly, we've put up an extra .pdf on the manning Arduino in Action site.
Hope that helps!