There is a web browser on the PS3, but you'll probably find it a bit awkward to use, especially with a controller. I think, though don't quote me on it, that you can connect any USB keyboard and mouse to the unit and use it with the web browser... But it lacks a lot of the basic features you will probably come to expect from desktop web browsers.
The web browser can go to essentially any website, though it may not work so well on some. Think of it kind of like a cell phone web browser on a game console.
Finally, I should point out that WEP encryption is pretty much useless. You really should upgrade that to WPA or WPA2 would be even better. WEP encryption, even a 128-bit key, can be broken in a matter of seconds. The only thing it really succeeds in doing is keeping out people who will respect the fact that you put a password on the connection because you didn't want others using it. In no way will it stop anyone from gaining access if they are so inclined.
OK I finally had to connect my PS3 to my wireless router to update it to play newer BluRay movies. Took some doing but finally got it to work and got it updated. What a pain entering the 26 character key for WEP! So now that I have access to the internet what can I do with it? Can I use/browse the whole internet or just certain things like Netflix (which I don't use or have). I don't think I need to use the Playstation store or play games on the internet. What esle is available to do?