Most of the routers, wireless or not, do not have the necessary dsl or cable modem built in. Some do, but they are usually expensive.
If your existing DSL modem connects to your computer using USB though, you're going to either have to get a router that accepts USB network input (expensive) or get another dsl modem that uses ethernet.
Don't get just a "wireless access point" unless you already have a router! Make sure it says router on it, not just wireless access point, otherwise it probably won't work unless you already have another router.
You may be able to find a wireless router for $49-$59 if you don't mind not getting the latest model, and a non-wireless router for as low as $30. I have 2 d-link wireless routers that work well for me, but I've also had some very bad luck lately with both cheap d-link and cheap linksys wireless routers when trying to set them up for family members. If you find one that *should* work but isn't, or it keeps dropping your connection, only spend a few days troubleshooting. Update the bios, try other settings, that sort of thing. If it still doesn't work, return it and get a different one.
As an example of something that *should* work but doesn't, My d-link DI-614+ works just great normally but if I turn on azureus bittorrent encryption, the wireless router starts acting strangely and then simply crashes after about 15 minutes. Routers shouldn't do that, but some are either poorly built or badly designed. I tried to install a D-Link DI-604 router for my grandfather but after each hour of use, it would crash requiring a reset. That's not acceptable. My Mom had a linksys WRT54G that worked just fine for 14 hours with WPA encryption turned on, but then when I reset the router to change the password, the wireless radio would not turn on unless I disabled WPA encryption. It would work with WEP encryption, but not the more secure WPA. I fixed that one by updating the bios, but it took several hours to troubleshoot something that should not have been a problem. I think I've heard these kinds of stories for every single brand of router, so just try one and if it won't work, troubleshoot for a little bit but do not be afraid to return it to try another one.
