You may want to take a look at the Linksys WRT series. The WRT platform is stable and solid, and are ready to go right out of the box, though of course you'll want to set up encryption on your network later.
If speed is a concern, remember that your connection out to the Internet is probably slower than 802.11b (11mbps though realistically lower), so you'll almost certainly have your Internet connection speed covered by an 802.11g router like the Linksys WRT54G. The WRT54G has five-star reviews all over the place, so I probably don't need to go over the specifics when plenty of other people have gone over them in more comprehensive detail.
If you're looking to make fast transfers from PC to PC on your network, you might want to look into an 802.11n router like the Linksys WRT160N. 802.11g will realistically get you somewhere between 24mbps and 48mbps depending on signal strength, whereas 802.11n delivers faster speeds over greater distances of up to
600mbps - typically you'll get somewhere between 100mbps and 300mbps, depending on how many channels a given .11n device uses. 802.11n is a relatively new technology, but it's also backwards-compatible with 802.11g, so you can buy an 802.11n router for the future and still be able to use 802.11g equipment with it. You can also upgrade to the WRT310N for gigabit Ethernet, if you want to wire a gigabit-enabled PC directly to the router (instead of using Wi-Fi), though this is probably overkill for your purposes.
As far as security goes, the software that runs on both the WRT54G and the WRT160N supports WPA2 data encryption, which at the moment is the best you can get without going proprietary. Both routers support a mixed WPA/WPA2 mode in the event that one or more of your PCs don't support WPA2. In all cases I would recommend against using WEP to do data encryption.
Like I said before, both routers I mentioned are ready to go out of the box. It looks like you're running Vista, which will let you set up a home network inside the Network and Sharing Center.
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