said by Whovian4life :Thank you so much for the quick response. I do want to have wireless internet because I'd like to be able to use it on my phone, tablet, or smart TV. How do I know if the modem has a built in router? I have researched many modems while deciding which one to buy, and none of them mention whether they have a built in router or not.
A Common Modem / Router would be The Surfboard SBG6580
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moto.arrisi.com/Video-So ··· /SBG6580Looking at Time Warner's supported modem/router list..
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www.amazon.com/Netgear-C ··· 08A2OG3CThe Netgear CG3000D is another modem/router combo.
You could always get a standalone modem to and hook a router to it.
My recommendation if your not real familiar with technology then just go with the modem/router lease from Time Warner -- Yes it's a small monthly fee but they will "troubleshoot it" , "help you set it up" and "replace it" if it dies.
If you use your own modem / router -- Your pretty much on your own for troubleshooting / tech support.