Hello, JudyAB35.
I would check with your CenturyLink support to see exactly what their service requires, especially when it comes to compatibility and best performance. There are some cable modem standards that you will want to make sure the router includes - some level of DOCSIS, for example.
Generally speaking, though, the device will be a combination modem/router and don't be surprised if wi-fi is standard fare these days. My C-Link service connects my devices via a wireless enabled modem/router here in Phoenix. It works well.
Check with your provider to see what they advise and provide. You don't have to buy/rent the gear they can supply, but you do want to know what is compatible with their service.