Didn't CenturyLink provide you with a modem? You should call CenturyLink and ask them what sort of modem you need. If they don't provide you a modem, you should be able to pick up DSL modems at any junk shop for <$10. Some can be used with CenturyLink. Others may be locked to a particular company.
The router (I believe most if not all routers) doesn't care what provider you use.
But, as was noted above, you still need a modem from CenturyLink.
Most modems are a combo modem-router, so it may not be fully necessary to have a separate router. Make sure you adjust your modem's settings to turn off it's router features if you do use a separate router, otherwise a few things may not work (I think it's generally gaming that doesn't like the double-NAT)
Most modem/routers given by the providers tend to have a cost associated for them to turn on the Wi-Fi. Actually cheaper to separate them.