I'd recommend this for a decently priced wireless router:
http://www.newegg.com/Product/Product.aspx?Item=N82E16833124010
There are a few different wireless types, 802.11a, 802.11b, 802.11g, and 802.11n are the most common. The 802.11 is just a code used by the IEEE (Institute of Electrical and Electronics Engineers) for Wi-Fi. Sort of like Firewire is sometimes called IEEE 1394.
The range of 802.11g is about 35 meters indoors. Obviously, walls and other things may obstruct the signal. Also note that the frequency of the signal is 2.4 GHz, so if you have any cordless phones or anything make sure they're not set at that frequency to prevent interference.
802.11g is the most used right now. It goes up to 54 Mbps. It's not the fastest, but it's more than enough for most people. 802.11n is the fastest at I think 270 Mbps, and has a bit longer range.
Wireless adapters can connect to your computer through PCI, USB, or a regular ethernet cable.
I have this:
http://www.newegg.com/Product/Product.aspx?Item=N82E16833130111
It's great for a pretty inexpensive solution. Small, fast, and gets a good signal. Works with Ubuntu and Vista too, which is always a plus.